In this paper, we consider the existence of three nontrivial solutions for a discrete non-linear multiparameter periodic problem involving the p-Laplacian. By using the similar method for the Dirichlet boundary value ...In this paper, we consider the existence of three nontrivial solutions for a discrete non-linear multiparameter periodic problem involving the p-Laplacian. By using the similar method for the Dirichlet boundary value problems in [C. Bonanno and P. Candito, Appl. Anal., 88（4） （2009）, pp. 605-616], we construct two new strong maximum principles and obtain that the boundary value problem has three positive solutions for λ and μ in some suitable intervals. The approaches we use are the critical point theory.展开更多
Rock fracture warning is one of the significant challenges in rock mechanics.Many true triaxial and synchronous acoustic emission(AE)tests were conducted on granite samples.The investigation focused on the characteris...Rock fracture warning is one of the significant challenges in rock mechanics.Many true triaxial and synchronous acoustic emission(AE)tests were conducted on granite samples.The investigation focused on the characteristics of AE signals preceding granite fracture,based on the critical slowing down(CSD)theory.The granite undergoes a transition from the stable phase to the fracture phase and exhibits a clear CSD phenomenon,characterized by a pronounced increase in variance and autocorrelation coefficient.The variance mutation points were found to be more identifiable and suitable as the primary criterion for predicting precursor information related to granite fracture,compared to the autocorrelation coefficient.It is noteworthy to emphasize that the CSD factor holds greater potential in elucidating the underlying mechanisms responsible for the critical transition of granite fracture,in comparison to the AE timing parameters.Furthermore,a novel multi-parameter collaborative prediction method for rock fracture was developed by comprehensively analyzing predictive information,including abnormal variation modes and the CSD factor of AE characteristic parameters.This method enhances the understanding and prediction of rock fracture-related geohazards.展开更多
A self-organized criticality model of a thermal sandpile is formulated for the first time to simulate the dynamic process with interaction between avalanche events on the fast time scale and diffusive transports on th...A self-organized criticality model of a thermal sandpile is formulated for the first time to simulate the dynamic process with interaction between avalanche events on the fast time scale and diffusive transports on the slow time scale. The main characteristics of the model are that both particle and energy avalanches of sand grains are considered simultaneously. Properties of intermittent transport and improved confinement are analyzed in detail. The results imply that the intermittent phenomenon such as blobs in the low confinement mode as well as edge localized modes in the high confinement mode observed in tokamak experiments are not only determined by the edge plasma physics, but also affected by the core plasma dynamics.展开更多
By means of CUSP model of catastrophe theory. this paper has studied thephysics process of rockburst occured on circular chamber. The present paper has nolonly described the instability process of rockburst more deepl...By means of CUSP model of catastrophe theory. this paper has studied thephysics process of rockburst occured on circular chamber. The present paper has nolonly described the instability process of rockburst more deeply. but also got the crilicaldepth of plastic softening area of chamber that is valuable in the controlling engineering of rockburst. the chamber displacement jump and energy liberation have been derived. the influence of rock parameters on the rockburst has been discussed .展开更多
As a core compulsory course for English majors majoring in teacher education,Literary Theory and Criticism plays an important role in enhancing text understanding,cultivating critical thinking,and shaping correct valu...As a core compulsory course for English majors majoring in teacher education,Literary Theory and Criticism plays an important role in enhancing text understanding,cultivating critical thinking,and shaping correct values in the future development of students.Influenced by traditional teaching ideas,students have many difficulties when learning this course,such as insufficient theoretical understanding,inadequate ability improvement,and not enough investment in course learning.In response to the above issues,this course focuses closely on the fundamental task of“cultivating virtue and nurturing people”,relying on modern information technology and introducing research methods of digital humanities.This course uses“7C”teaching mode under the“three-level integration”,in which“teaching”and“education”are carried out synchronously,and“teacher”and“student”are developed together,in order to greatly enhance students’learning participation and course satisfaction.展开更多
In this paper, we intend to consider a kind of nonlinear Klein-Gordon equation coupled with Born-Infeld theory. By using critical point theory and the method of Nehari manifold, we obtain two existing results of infin...In this paper, we intend to consider a kind of nonlinear Klein-Gordon equation coupled with Born-Infeld theory. By using critical point theory and the method of Nehari manifold, we obtain two existing results of infinitely many high-energy radial solutions and a ground-state solution for this kind of system, which improve and generalize some related results in the literature.展开更多
In 2014,Huang Kaihong,a professor at School of Foreign Languages and Cultures,Southwest University of Science and Technology,interviewed the Doctoral advisor Professor Nie Zhenzhao during the period of his academic vi...In 2014,Huang Kaihong,a professor at School of Foreign Languages and Cultures,Southwest University of Science and Technology,interviewed the Doctoral advisor Professor Nie Zhenzhao during the period of his academic visiting to Central China Normal University.As early as in 2005,Huang Kaihong conducted an interview with Professor Nie Zhenzhao on the topic of the general introduction of ethical literary criticism.So around 11 years later,the second interview mainly covers not only the ethical literary criticism theory,but the game theory and the relationship between them as well.Professor Nie thinks whether the game theory can be applied to literature research is still under discussion.The theory of ethical literary criticism is a kind of methodology based on science and it can get the attention of literary critics at home and abroad,which is because it fits the practical needs of literary criticism,draws the literary criticism away from only emphasizing criticism genres and the research of criticism terms,and pays attention to the true nature of the literary text in literature research.After consulting Professor Nie Zhenzhao about some related questions from the perspective of game theory.Huang Kaihong gets some significant information concerning literature research and understands the latest core terms and the concrete application method of ethical literary criticism,especially the relationship between the instructing and aesthetic functions of literature.展开更多
The Turmin argument model consists of six basic elements: data (datum), support (backing), reason (warrant), limit (qualifier), rebuttal (rebutal) and claim (claim). The basic process of its argument and critical read...The Turmin argument model consists of six basic elements: data (datum), support (backing), reason (warrant), limit (qualifier), rebuttal (rebutal) and claim (claim). The basic process of its argument and critical reading both point to the cultivation of multi-dimensional questioning and dialectical problem analysis and choice ability in critical thinking, and its core goal is the same. Therefore, teachers can choose suitable English argumentative materials inside and outside class for high school students, and build the teaching model of "ask-theory-exhibition-evaluation" based on the Tu-Min demonstration model, so as to more effectively improve high school students ability to ask questions and dialectically analyze problems and judge independently in their critical thinking.展开更多
Theoretical Studies in Literature and Art(ISSN 0257-0254)is a most highly-recognized peer-reviewed journal in China,and has been listed in Scopus and Ebsco.TSLA,launched in 1980 bimonthly,publishes original articles i...Theoretical Studies in Literature and Art(ISSN 0257-0254)is a most highly-recognized peer-reviewed journal in China,and has been listed in Scopus and Ebsco.TSLA,launched in 1980 bimonthly,publishes original articles in Chinese or English in arts and humanities,especially literary studies.We cover any topic/issue involving,of.about or on but not confined to China in the fields of literary theory,critical theory,aesthetics,philosophy of art,cultural studies,etc.展开更多
Theoretical Studies in Literature and Art(ISSN 0257-0254)is a most highly-recognized peer-reviewed journal in China,and has been listed in Scopus and Ebsco.TSLA,launched in 1980 bimonthly,publishes original articles i...Theoretical Studies in Literature and Art(ISSN 0257-0254)is a most highly-recognized peer-reviewed journal in China,and has been listed in Scopus and Ebsco.TSLA,launched in 1980 bimonthly,publishes original articles in Chinese or English in arts and humanities,especially literary studies.We cover any topic/issue involving,of,about or on but not confined to China in the fields of literary theory,critical theory,aesthetics,philosophy of art,cultural studies,etc.展开更多
Theoretical Studies in Literature and Art (ISSN 0257-0254) is a most highly-recognized peer-reviewed journal in China,and has been listed in Scopus and Ebsco.TSLA,launched in 1980 bimonthly,publishes original articles...Theoretical Studies in Literature and Art (ISSN 0257-0254) is a most highly-recognized peer-reviewed journal in China,and has been listed in Scopus and Ebsco.TSLA,launched in 1980 bimonthly,publishes original articles in Chinese or English in arts and humanities,especially literary studies.We cover any topic/issue involving,of,about or on but not confined to China in the fields of literary theory,critical theory,aesthetics,philosophy of art,cultural studies,etc.展开更多
Heavy-duty freight railway axles are no less important than those of passenger trains,owing to the potentially catastrophic results caused by the derailment of trains carrying hazardous substances.Intrinsic and extrin...Heavy-duty freight railway axles are no less important than those of passenger trains,owing to the potentially catastrophic results caused by the derailment of trains carrying hazardous substances.Intrinsic and extrinsic imperfections challenge classical design theories built based on the safe life concept,and damage tolerance assessment becomes vital for the safety and reliability of long-term serviced railway axles,as pits and scratches are common defects for heavy-duty railway axles.In this work,four-point rotating bending fatigue tests of AAR-CM railway axle steel specimens with semicircular and circumferential groove notches are conducted.The fatigue limit of the semicircular notched specimens was evaluated based on fracture mechanics theory,in which non-conservative results are obtained by the El Haddad model and the S–N curves of circumferential groove notched specimens are correlated by the theory of critical distance(TCD).展开更多
In In the Castle of My Skin （hereafter Castle） （1983）, the littoral as trope provides a means for discovering Lamming＇s authorial license, one that speaks to postcolonial and phenomenological aims. In this semi-a...In In the Castle of My Skin （hereafter Castle） （1983）, the littoral as trope provides a means for discovering Lamming＇s authorial license, one that speaks to postcolonial and phenomenological aims. In this semi-autobiographical novel, Lamming examines self-awareness and the process through which language and self-analysis may take shape on or be inspired by the shore＇s edge. Through the telling of personal stories, discussions of a colonial history, and with allusions to the social privations affecting the immediate community, Lamming represents the changing realities, the main characters （＂G＂ and his friends） experience as they become socially aware; he highlights this transformative rise to consciousness through the use of littoral imagery in Chapters Six, Eleven, and Fourteen. In this essay, the author explores these representations using postcolonial, psychoanalytical, and phenomenological approaches, giving particular attention to Chapter Six, the longer chapter where Lamming creates a blueprint of the issues to which he will return in Chapters Eleven and Fourteen. Castle epitomizes the ways in which the littoral as trope has the potential to symbolically impact an author＇s text, especially a means for crafting an authorial language that demonstrates a young man＇s rise to consciousness and self-actualization on the shorelines of Barbados before he emigrates abroad.展开更多
Existing critical point theories including metric and topological critical point theories are difficult to be applied directly to some concrete problems in particular polyhedral settings,because the notions of critica...Existing critical point theories including metric and topological critical point theories are difficult to be applied directly to some concrete problems in particular polyhedral settings,because the notions of critical sets could be either very vague or too large.To overcome these difficulties,we develop the critical point theory for nonsmooth but Lipschitzian functions defined on convex polyhedrons.This yields natural extensions of classical results in the critical point theory,such as the Liusternik-Schnirelmann multiplicity theorem.More importantly,eigenvectors for some eigenvalue problems involving graph 1-Laplacian coincide with critical points of the corresponding functions on polytopes,which indicates that the critical point theory proposed in the present paper can be applied to study the nonlinear spectral graph theory.展开更多
In order to study the water-inrush mechanism of concealed collapse pillars from the mechanical view, a mechanical model for water-inrush of collapse pillars has been established based on thick plate theory of elastic ...In order to study the water-inrush mechanism of concealed collapse pillars from the mechanical view, a mechanical model for water-inrush of collapse pillars has been established based on thick plate theory of elastic mechanics in this paper.By solving this model the deformation of water-resistant rock strata under the action of water pressure and the expression of critical water pressure for collapse pillar waterinrush have been obtained The research results indicate that：the boundary conditions and strength of water-resistant strata play important roles in influencing water-inrush of collapse pillars.The critical water-inrush pressure is determined by both relative thickness and absolute thickness of water-resistant strata.展开更多
The purpose of this paper is to investigate a nonlocal Dirichlet problem with(p(x),q(x))-Laplacian-like operator originated from a capillary phenomena.Using the variational methods and the critical point theory,we est...The purpose of this paper is to investigate a nonlocal Dirichlet problem with(p(x),q(x))-Laplacian-like operator originated from a capillary phenomena.Using the variational methods and the critical point theory,we establish the existence of infinitely many weak solutions for this problem.展开更多
In this paper we investigate a class of impulsive differential equations with Dirichlet boundary conditions. Firstly, we define new inner product of <img src="Edit_890fce38-e82b-4f36-be40-9d05e8119b88.png"...In this paper we investigate a class of impulsive differential equations with Dirichlet boundary conditions. Firstly, we define new inner product of <img src="Edit_890fce38-e82b-4f36-be40-9d05e8119b88.png" width="40" height="17" alt="" /> and prove that the norm which is deduced by the inner product is equivalent to the usual norm. Secondly, we construct the lower and upper solutions of (1.1). Thirdly, we obtain the existence of a positive solution, a negative solution and a sign-changing solution by using critical point theory and variational methods. Finally, an example is presented to illustrate the application of our main result.展开更多
In this work,the solvability of a class of second-order Hamiltonian systems on time scales is generalized to non-local boundary conditions.The measurements obtained by non-local conditions are more accurate than those...In this work,the solvability of a class of second-order Hamiltonian systems on time scales is generalized to non-local boundary conditions.The measurements obtained by non-local conditions are more accurate than those given by local conditions in some problems.Compared with the known results,this work establishes the variational structure in an appropriate Sobolev’s space.Then,by applying the mountain pass theorem and symmetric mountain pass theorem,the existence and multiplicity of the solutions are obtained.Finally,some examples with numerical simulation results are given to illustrate the correctness of the results obtained.展开更多
In this article we consider via critical point theory the existence of homoclinic orbits of the first-order differential difference equation z（t）＋B（t）z（t）＋f（t,z（t＋τ）,z（t）,z（t-τ））=0.
基金Supported by NSFC(11326127,11101335)NWNULKQN-11-23the Fundamental Research Funds for the Gansu Universities
文摘In this paper, we consider the existence of three nontrivial solutions for a discrete non-linear multiparameter periodic problem involving the p-Laplacian. By using the similar method for the Dirichlet boundary value problems in [C. Bonanno and P. Candito, Appl. Anal., 88（4） （2009）, pp. 605-616], we construct two new strong maximum principles and obtain that the boundary value problem has three positive solutions for λ and μ in some suitable intervals. The approaches we use are the critical point theory.
基金Project(52074294)supported by the National Natural Science Foundation of ChinaProject(2022YJSNY16)supported by the Fundamental Research Funds for the Central Universities,China。
文摘Rock fracture warning is one of the significant challenges in rock mechanics.Many true triaxial and synchronous acoustic emission(AE)tests were conducted on granite samples.The investigation focused on the characteristics of AE signals preceding granite fracture,based on the critical slowing down(CSD)theory.The granite undergoes a transition from the stable phase to the fracture phase and exhibits a clear CSD phenomenon,characterized by a pronounced increase in variance and autocorrelation coefficient.The variance mutation points were found to be more identifiable and suitable as the primary criterion for predicting precursor information related to granite fracture,compared to the autocorrelation coefficient.It is noteworthy to emphasize that the CSD factor holds greater potential in elucidating the underlying mechanisms responsible for the critical transition of granite fracture,in comparison to the AE timing parameters.Furthermore,a novel multi-parameter collaborative prediction method for rock fracture was developed by comprehensively analyzing predictive information,including abnormal variation modes and the CSD factor of AE characteristic parameters.This method enhances the understanding and prediction of rock fracture-related geohazards.
基金Supported by the National Natural Science Foundation of China under Grant No 11275061the National Magnetic Confinement Fusion Science Program under Grant No 2014GB108002
文摘A self-organized criticality model of a thermal sandpile is formulated for the first time to simulate the dynamic process with interaction between avalanche events on the fast time scale and diffusive transports on the slow time scale. The main characteristics of the model are that both particle and energy avalanches of sand grains are considered simultaneously. Properties of intermittent transport and improved confinement are analyzed in detail. The results imply that the intermittent phenomenon such as blobs in the low confinement mode as well as edge localized modes in the high confinement mode observed in tokamak experiments are not only determined by the edge plasma physics, but also affected by the core plasma dynamics.
文摘By means of CUSP model of catastrophe theory. this paper has studied thephysics process of rockburst occured on circular chamber. The present paper has nolonly described the instability process of rockburst more deeply. but also got the crilicaldepth of plastic softening area of chamber that is valuable in the controlling engineering of rockburst. the chamber displacement jump and energy liberation have been derived. the influence of rock parameters on the rockburst has been discussed .
基金supported by Henan Province Teaching Reform and Practice Project(Project Fund No.135)—Research on the Reform of Literary Theory Courses for English Majors in Universities.
文摘As a core compulsory course for English majors majoring in teacher education,Literary Theory and Criticism plays an important role in enhancing text understanding,cultivating critical thinking,and shaping correct values in the future development of students.Influenced by traditional teaching ideas,students have many difficulties when learning this course,such as insufficient theoretical understanding,inadequate ability improvement,and not enough investment in course learning.In response to the above issues,this course focuses closely on the fundamental task of“cultivating virtue and nurturing people”,relying on modern information technology and introducing research methods of digital humanities.This course uses“7C”teaching mode under the“three-level integration”,in which“teaching”and“education”are carried out synchronously,and“teacher”and“student”are developed together,in order to greatly enhance students’learning participation and course satisfaction.
文摘In this paper, we intend to consider a kind of nonlinear Klein-Gordon equation coupled with Born-Infeld theory. By using critical point theory and the method of Nehari manifold, we obtain two existing results of infinitely many high-energy radial solutions and a ground-state solution for this kind of system, which improve and generalize some related results in the literature.
文摘In 2014,Huang Kaihong,a professor at School of Foreign Languages and Cultures,Southwest University of Science and Technology,interviewed the Doctoral advisor Professor Nie Zhenzhao during the period of his academic visiting to Central China Normal University.As early as in 2005,Huang Kaihong conducted an interview with Professor Nie Zhenzhao on the topic of the general introduction of ethical literary criticism.So around 11 years later,the second interview mainly covers not only the ethical literary criticism theory,but the game theory and the relationship between them as well.Professor Nie thinks whether the game theory can be applied to literature research is still under discussion.The theory of ethical literary criticism is a kind of methodology based on science and it can get the attention of literary critics at home and abroad,which is because it fits the practical needs of literary criticism,draws the literary criticism away from only emphasizing criticism genres and the research of criticism terms,and pays attention to the true nature of the literary text in literature research.After consulting Professor Nie Zhenzhao about some related questions from the perspective of game theory.Huang Kaihong gets some significant information concerning literature research and understands the latest core terms and the concrete application method of ethical literary criticism,especially the relationship between the instructing and aesthetic functions of literature.
文摘The Turmin argument model consists of six basic elements: data (datum), support (backing), reason (warrant), limit (qualifier), rebuttal (rebutal) and claim (claim). The basic process of its argument and critical reading both point to the cultivation of multi-dimensional questioning and dialectical problem analysis and choice ability in critical thinking, and its core goal is the same. Therefore, teachers can choose suitable English argumentative materials inside and outside class for high school students, and build the teaching model of "ask-theory-exhibition-evaluation" based on the Tu-Min demonstration model, so as to more effectively improve high school students ability to ask questions and dialectically analyze problems and judge independently in their critical thinking.
文摘Theoretical Studies in Literature and Art(ISSN 0257-0254)is a most highly-recognized peer-reviewed journal in China,and has been listed in Scopus and Ebsco.TSLA,launched in 1980 bimonthly,publishes original articles in Chinese or English in arts and humanities,especially literary studies.We cover any topic/issue involving,of.about or on but not confined to China in the fields of literary theory,critical theory,aesthetics,philosophy of art,cultural studies,etc.
文摘Theoretical Studies in Literature and Art(ISSN 0257-0254)is a most highly-recognized peer-reviewed journal in China,and has been listed in Scopus and Ebsco.TSLA,launched in 1980 bimonthly,publishes original articles in Chinese or English in arts and humanities,especially literary studies.We cover any topic/issue involving,of,about or on but not confined to China in the fields of literary theory,critical theory,aesthetics,philosophy of art,cultural studies,etc.
文摘Theoretical Studies in Literature and Art (ISSN 0257-0254) is a most highly-recognized peer-reviewed journal in China,and has been listed in Scopus and Ebsco.TSLA,launched in 1980 bimonthly,publishes original articles in Chinese or English in arts and humanities,especially literary studies.We cover any topic/issue involving,of,about or on but not confined to China in the fields of literary theory,critical theory,aesthetics,philosophy of art,cultural studies,etc.
基金Supported by National Natural Science Foundation of China(Grant No.12232004)Guangdong Provincial Basic and Applied Basic Research Foundation(Grant No.2022A1515140111)+1 种基金Anhui Provincial Science and Technology Projects(Grant No.JB24075)Sichuan Provincial Science and Technology Program(Grant Nos.2024NSFSC2020,2023YFG0234)。
文摘Heavy-duty freight railway axles are no less important than those of passenger trains,owing to the potentially catastrophic results caused by the derailment of trains carrying hazardous substances.Intrinsic and extrinsic imperfections challenge classical design theories built based on the safe life concept,and damage tolerance assessment becomes vital for the safety and reliability of long-term serviced railway axles,as pits and scratches are common defects for heavy-duty railway axles.In this work,four-point rotating bending fatigue tests of AAR-CM railway axle steel specimens with semicircular and circumferential groove notches are conducted.The fatigue limit of the semicircular notched specimens was evaluated based on fracture mechanics theory,in which non-conservative results are obtained by the El Haddad model and the S–N curves of circumferential groove notched specimens are correlated by the theory of critical distance(TCD).
文摘In In the Castle of My Skin （hereafter Castle） （1983）, the littoral as trope provides a means for discovering Lamming＇s authorial license, one that speaks to postcolonial and phenomenological aims. In this semi-autobiographical novel, Lamming examines self-awareness and the process through which language and self-analysis may take shape on or be inspired by the shore＇s edge. Through the telling of personal stories, discussions of a colonial history, and with allusions to the social privations affecting the immediate community, Lamming represents the changing realities, the main characters （＂G＂ and his friends） experience as they become socially aware; he highlights this transformative rise to consciousness through the use of littoral imagery in Chapters Six, Eleven, and Fourteen. In this essay, the author explores these representations using postcolonial, psychoanalytical, and phenomenological approaches, giving particular attention to Chapter Six, the longer chapter where Lamming creates a blueprint of the issues to which he will return in Chapters Eleven and Fourteen. Castle epitomizes the ways in which the littoral as trope has the potential to symbolically impact an author＇s text, especially a means for crafting an authorial language that demonstrates a young man＇s rise to consciousness and self-actualization on the shorelines of Barbados before he emigrates abroad.
基金supported by National Natural Science Foundation of China(Grant Nos.11822102 and 11421101)supported by Beijing Academy of Artificial Intelligence(BAAI)supported by the project funded by China Postdoctoral Science Foundation(Grant No.BX201700009)。
文摘Existing critical point theories including metric and topological critical point theories are difficult to be applied directly to some concrete problems in particular polyhedral settings,because the notions of critical sets could be either very vague or too large.To overcome these difficulties,we develop the critical point theory for nonsmooth but Lipschitzian functions defined on convex polyhedrons.This yields natural extensions of classical results in the critical point theory,such as the Liusternik-Schnirelmann multiplicity theorem.More importantly,eigenvectors for some eigenvalue problems involving graph 1-Laplacian coincide with critical points of the corresponding functions on polytopes,which indicates that the critical point theory proposed in the present paper can be applied to study the nonlinear spectral graph theory.
基金Projects are supported by the National Basic Research Program of China(No.2007CB209400)the National Natural Science Foundation of China(Nos.50974115,50904065 and 50974107)the 111 Project(No.B07028).
文摘In order to study the water-inrush mechanism of concealed collapse pillars from the mechanical view, a mechanical model for water-inrush of collapse pillars has been established based on thick plate theory of elastic mechanics in this paper.By solving this model the deformation of water-resistant rock strata under the action of water pressure and the expression of critical water pressure for collapse pillar waterinrush have been obtained The research results indicate that：the boundary conditions and strength of water-resistant strata play important roles in influencing water-inrush of collapse pillars.The critical water-inrush pressure is determined by both relative thickness and absolute thickness of water-resistant strata.
基金Supported by the Fundamental Research Funds for the Central Universities(Grant No.31920180041)the Fund for Talent Introduction of Northwest Minzu University(Grant No.xbmuyjrc201907)。
文摘The purpose of this paper is to investigate a nonlocal Dirichlet problem with(p(x),q(x))-Laplacian-like operator originated from a capillary phenomena.Using the variational methods and the critical point theory,we establish the existence of infinitely many weak solutions for this problem.
文摘In this paper we investigate a class of impulsive differential equations with Dirichlet boundary conditions. Firstly, we define new inner product of <img src="Edit_890fce38-e82b-4f36-be40-9d05e8119b88.png" width="40" height="17" alt="" /> and prove that the norm which is deduced by the inner product is equivalent to the usual norm. Secondly, we construct the lower and upper solutions of (1.1). Thirdly, we obtain the existence of a positive solution, a negative solution and a sign-changing solution by using critical point theory and variational methods. Finally, an example is presented to illustrate the application of our main result.
基金Project supported by the National Natural Science Foundation of China(No.11571207)the Natural Science Foundation of Shandong Province of China(Nos.ZR2021MA064 and ZR2020MA017)the Taishan Scholar Project of Shandong Province of China。
文摘In this work,the solvability of a class of second-order Hamiltonian systems on time scales is generalized to non-local boundary conditions.The measurements obtained by non-local conditions are more accurate than those given by local conditions in some problems.Compared with the known results,this work establishes the variational structure in an appropriate Sobolev’s space.Then,by applying the mountain pass theorem and symmetric mountain pass theorem,the existence and multiplicity of the solutions are obtained.Finally,some examples with numerical simulation results are given to illustrate the correctness of the results obtained.
基金supported by National Natural Science Foundation of China(51275094)by High-Level Personnel Project of Guangdong Province(2014011)by China Postdoctoral Science Foundation(20110490893)
文摘In this article we consider via critical point theory the existence of homoclinic orbits of the first-order differential difference equation z（t）＋B（t）z（t）＋f（t,z（t＋τ）,z（t）,z（t-τ））=0.
