In reliability analyses,the absence of a priori information on the most probable point of failure(MPP)may result in overlooking critical points,thereby leading to biased assessment outcomes.Moreover,second-order relia...In reliability analyses,the absence of a priori information on the most probable point of failure(MPP)may result in overlooking critical points,thereby leading to biased assessment outcomes.Moreover,second-order reliability methods exhibit limited accuracy in highly nonlinear scenarios.To overcome these challenges,a novel reliability analysis strategy based on a multimodal differential evolution algorithm and a hypersphere integration method is proposed.Initially,the penalty function method is employed to reformulate the MPP search problem as a conditionally constrained optimization task.Subsequently,a differential evolution algorithm incorporating a population delineation strategy is utilized to identify all MPPs.Finally,a paraboloid equation is constructed based on the curvature of the limit-state function at the MPPs,and the failure probability of the structure is calculated by using the hypersphere integration method.The localization effectiveness of the MPPs is compared through multiple numerical cases and two engineering examples,with accuracy comparisons of failure probabilities against the first-order reliability method(FORM)and the secondorder reliability method(SORM).The results indicate that the method effectively identifies existing MPPs and achieves higher solution precision.展开更多
The oscillatory behavior of neutral differential equation with positive and negative coefficients is investigated by mathematics analysis technique and the fixed point principle. Some sufficient conditions for oscilla...The oscillatory behavior of neutral differential equation with positive and negative coefficients is investigated by mathematics analysis technique and the fixed point principle. Some sufficient conditions for oscillation of neutral differential equation with positive and negative coefficients are obtained.展开更多
By means of an abstract continuation theorem, the existence criteria are established for the positive periodic solutions of a neutral functional differential equation d N d t=N(t)[a(t)-β(t)N(t)-b(t)N(t-σ(t))-c(...By means of an abstract continuation theorem, the existence criteria are established for the positive periodic solutions of a neutral functional differential equation d N d t=N(t)[a(t)-β(t)N(t)-b(t)N(t-σ(t))-c(t)N′(t-τ(t))].展开更多
In this paper,we study a Dirichlet-type boundary value problem(BVP) of nonlinear fractional differential equation with an order α∈(3,4],where the fractional derivative D~α_(o^+)is the standard Riemann-Liouville fra...In this paper,we study a Dirichlet-type boundary value problem(BVP) of nonlinear fractional differential equation with an order α∈(3,4],where the fractional derivative D~α_(o^+)is the standard Riemann-Liouville fractional derivative.By constructing the Green function and investigating its properties,we obtain some criteria for the existence of one positive solution and two positive solutions for the above BVP.The Krasnosel'skii fixedpoint theorem in cones is used here.We also give an example to illustrate the applicability of our results.展开更多
In this paper,the boundary value problems of p-Laplacian functional differential equation are studied.By using a fixed point theorem in cones,some criteria for the existence of positive solutions are given.
A class of second order nonlinear differential equations with delay depenging on the unknown function of the fromin the case where ∫0∞ ds/r(s) < ∞ is studied. Various classifications of their eventually positive...A class of second order nonlinear differential equations with delay depenging on the unknown function of the fromin the case where ∫0∞ ds/r(s) < ∞ is studied. Various classifications of their eventually positive solutions are given in terms of their asymptotic magnitudes, and necessary as well as sufficient conditions for the existence of these solutions are also obtained.展开更多
In this article, the existence and uniqueness of positive solution for a class of nonlinear fractional differential equations is proved by constructing the upper and lower control functions of the nonlinear term witho...In this article, the existence and uniqueness of positive solution for a class of nonlinear fractional differential equations is proved by constructing the upper and lower control functions of the nonlinear term without any monotone requirement. Our main method to the problem is the method of upper and lower solutions and Schauder fixed point theorem. Finally, we give an example to illuminate our results.展开更多
Aim To investigate the existence of positive solutions for impulsive neutral differential equations. Methods The Banach contraction principle was used to establish our results. Results and Conclusion The results of...Aim To investigate the existence of positive solutions for impulsive neutral differential equations. Methods The Banach contraction principle was used to establish our results. Results and Conclusion The results of the existence of positive solutions for impulsive neutral differential equations are obtained.展开更多
This article considers the Dirichlet problem of homogeneous and inhomogeneous second-order ordinary differential systems. A nondegeneracy result is proven for positive solutions of homogeneous systems. Sufficient and ...This article considers the Dirichlet problem of homogeneous and inhomogeneous second-order ordinary differential systems. A nondegeneracy result is proven for positive solutions of homogeneous systems. Sufficient and necessary conditions for the existence of multiple positive solutions for inhomogeneous systems are obtained by making use of the nondegeneracy and uniqueness results of homogeneous systems.展开更多
In this paper, we consider the positive solutions of fractional three-point boundary value problem of the form Dο^α＋u（t）＋f（t,u（t）,u＇（t）,…,u^（n-3）（5）,u^（n-2）（t））=0,u^（i）（0）=0,0≤i≤n-2,u^（n-...In this paper, we consider the positive solutions of fractional three-point boundary value problem of the form Dο^α＋u（t）＋f（t,u（t）,u＇（t）,…,u^（n-3）（5）,u^（n-2）（t））=0,u^（i）（0）=0,0≤i≤n-2,u^（n-2）（1）-βu^（n-2）（ξ）=0,where 0〈t〈1,n-1〈α≤n,n≥2,ξ Е（0,1）,βξ^a-n〈1. We first transform it into another equivalent boundary value problem. Then, we derive the Green＇s function for the equivalent boundary value problem and show that it satisfies certain properties. At last, by using some fixed-point theorems, we obtain the existence of positive solution for this problem. Example is given to illustrate the effectiveness of our result.展开更多
By utilizing a fixed point theorem on cone, some new results on the existence ofpositive periodic solutions for nonautonomous differential equations with delay are derived.
In this paper, we investigate the existence of multiple positive periodic solutions for functional differential equations with infinite delay by applying the Krasnoselskii fixed point theorem for cone map and the Legg...In this paper, we investigate the existence of multiple positive periodic solutions for functional differential equations with infinite delay by applying the Krasnoselskii fixed point theorem for cone map and the Leggett-Williams fixed point theorem.展开更多
This paper deals with the existence of positive periodic solutions for a kind of nonautonomous Volterra intergo-differential equations by employing the Krasnoselskii fixed point theorem. Applying the general theorems ...This paper deals with the existence of positive periodic solutions for a kind of nonautonomous Volterra intergo-differential equations by employing the Krasnoselskii fixed point theorem. Applying the general theorems established to several biomathematical models, the paper improves some previous results and obtains some new results.展开更多
BACKGROUND The log odds of positive lymph nodes(LODDS)are correlated with survival outcomes in gastric cancer(GC)patients.However,the prognostic value across different tumor differentiation levels remains unclear.AIM ...BACKGROUND The log odds of positive lymph nodes(LODDS)are correlated with survival outcomes in gastric cancer(GC)patients.However,the prognostic value across different tumor differentiation levels remains unclear.AIM To evaluate the independent prognostic value of LODDS and the stratified predictive efficacy in GC patients with different histologic differentiations.METHODS We conducted a retrospective analysis of 2103 GC patients who underwent radical gastrectomy at Zhejiang Cancer Hospital.The prognostic value of LODDS was compared with that of other lymph node-based metrics,including the pathologic N stage,number of positive lymph nodes,number of total lymph nodes,and lymph node ratio,stratified by tumor differentiation.RESULTS LODDS was identified as an independent prognostic factor for overall survival in moderately to poorly differentiated GC patients.LODDS demonstrated superior predictive accuracy over other lymph node metrics.A nomogram incorporating LODDS,age,carbohydrate antigen(CA)125,carcinoembryonic antigen,and tumor differentiation showed good predictive accuracy(C-index=0.703).A higher LODDS was significantly associated with an increased risk of recurrence or metastasis,poorly differentiated tumors,advanced cancer,mucinous gastric adenocarcinoma,nerve invasion,and vascular tumor thrombus.Additionally,LODDS was positively correlated with the tumor markers CA19-9,CA72-4,CA125,and CA242(all P<0.05).CONCLUSION LODDS is an independent prognostic indicator for patients with moderately and poorly differentiated GC,and its predictive performance is superior to that of other models.展开更多
In this paper, we study a class of singular fractional differential system with Riemann-Stieltjes integral boundary condition by constructing a new cone and using Leggett-Williams fixed point theorem. The existence of...In this paper, we study a class of singular fractional differential system with Riemann-Stieltjes integral boundary condition by constructing a new cone and using Leggett-Williams fixed point theorem. The existence of multiple positive solutions is obtained. An example is presented to illustrate our main results.展开更多
The nonlinear differential equationx′(t)=-δ(t)x(t)+f(t,x(t))(*)is considered,where δ(t) is a periodic function of periodic T,f(t,x) is continuous and periodic in t.It is showed that (*) has at least two positive T-...The nonlinear differential equationx′(t)=-δ(t)x(t)+f(t,x(t))(*)is considered,where δ(t) is a periodic function of periodic T,f(t,x) is continuous and periodic in t.It is showed that (*) has at least two positive T-periodic solutions under certain growth conditions imposed on f.Applications will be presented to illustrate the main results.展开更多
Sorting and collecting the data by questionnaire survey and literature analysis,the childrenswear brand elemental analysis is completed.The development goal of differentiated positioning of Chinese childrenswear brand...Sorting and collecting the data by questionnaire survey and literature analysis,the childrenswear brand elemental analysis is completed.The development goal of differentiated positioning of Chinese childrenswear brands is decided.Four modules which influence the brand differentiated development were extracted to establish the hierarchical analysis framework for the differentiated positioning development of Chinese childrenswear brand.Judgment matrix diagram is constructed by using the analytic hierarchy process(AHP).According to the data analysis and judgment,the core elements,basic elements and auxiliary elements are identified which support the development of differentiated positioning of Chinese childrenswear brands.The clear development path of differentiated positioning of Chinese childrenswear brands is formed,namely to enhance the core essential factors as the key point,to grasp the elements’spirit exactly in differentiated positioning of brand style,childrenswear color feature,green and security of products quality and retail prices which influence the brand differentiated development.The Chinese existing technical advantages was given full play by providing the basic support for the differentiated development of childrenswear brands.Auxiliary elements were heleped to grow by making auxiliary elements play a greater role.The goal was achieved to improve the market competitiveness by development of differentiated positioning of Chinese childrenswear brands.展开更多
This paper is to obtain sufficient conditions under which the neutral functional differential equation d/dx[x(t) + integral(c)(t) x(s)d(s) mu(t, s)] + integral(c)(t) f(t, x(s))d(s) eta(t, s) = 0, t greater than or equ...This paper is to obtain sufficient conditions under which the neutral functional differential equation d/dx[x(t) + integral(c)(t) x(s)d(s) mu(t, s)] + integral(c)(t) f(t, x(s))d(s) eta(t, s) = 0, t greater than or equal to t(0) greater than or equal to c (1) has a positive solution on [c, +infinity). Some results in [1] are generalized. Then we apply our results to functional differential equations of special form and obtain sufficient conditions for those equations to have a positive solution.展开更多
In this paper, existence of multiple positive solutions for fractional differential equations in Banach spaces is obtained by utilizing the fixed point index theory of completely continuous operators.
This paper is to investigate the positive solutions of the systems of second-order ordinary differential equations with nonhomogeneous multi-point boundary conditions. By the lower and upper solutions method, Schauder...This paper is to investigate the positive solutions of the systems of second-order ordinary differential equations with nonhomogeneous multi-point boundary conditions. By the lower and upper solutions method, Schauder fixed point theorem and fixed point index theory, under certain conditions, it is proved that there exist appropriate regions of parameters in which the problem has at least two, at least one or no positive solution.展开更多
基金National Natural Science Foundation of China(No.52375236)Fundamental Research Funds for the Central Universities of China(No.23D110316)。
文摘In reliability analyses,the absence of a priori information on the most probable point of failure(MPP)may result in overlooking critical points,thereby leading to biased assessment outcomes.Moreover,second-order reliability methods exhibit limited accuracy in highly nonlinear scenarios.To overcome these challenges,a novel reliability analysis strategy based on a multimodal differential evolution algorithm and a hypersphere integration method is proposed.Initially,the penalty function method is employed to reformulate the MPP search problem as a conditionally constrained optimization task.Subsequently,a differential evolution algorithm incorporating a population delineation strategy is utilized to identify all MPPs.Finally,a paraboloid equation is constructed based on the curvature of the limit-state function at the MPPs,and the failure probability of the structure is calculated by using the hypersphere integration method.The localization effectiveness of the MPPs is compared through multiple numerical cases and two engineering examples,with accuracy comparisons of failure probabilities against the first-order reliability method(FORM)and the secondorder reliability method(SORM).The results indicate that the method effectively identifies existing MPPs and achieves higher solution precision.
文摘The oscillatory behavior of neutral differential equation with positive and negative coefficients is investigated by mathematics analysis technique and the fixed point principle. Some sufficient conditions for oscillation of neutral differential equation with positive and negative coefficients are obtained.
基金National Natural Science Foundation of China( 198710 0 5 )
文摘By means of an abstract continuation theorem, the existence criteria are established for the positive periodic solutions of a neutral functional differential equation d N d t=N(t)[a(t)-β(t)N(t)-b(t)N(t-σ(t))-c(t)N′(t-τ(t))].
基金Supported by the Research Fund for the Doctoral Program of High Education of China(20094407110001)Supported by the NSF of Guangdong Province(10151063101000003)
文摘In this paper,we study a Dirichlet-type boundary value problem(BVP) of nonlinear fractional differential equation with an order α∈(3,4],where the fractional derivative D~α_(o^+)is the standard Riemann-Liouville fractional derivative.By constructing the Green function and investigating its properties,we obtain some criteria for the existence of one positive solution and two positive solutions for the above BVP.The Krasnosel'skii fixedpoint theorem in cones is used here.We also give an example to illustrate the applicability of our results.
文摘In this paper,the boundary value problems of p-Laplacian functional differential equation are studied.By using a fixed point theorem in cones,some criteria for the existence of positive solutions are given.
文摘A class of second order nonlinear differential equations with delay depenging on the unknown function of the fromin the case where ∫0∞ ds/r(s) < ∞ is studied. Various classifications of their eventually positive solutions are given in terms of their asymptotic magnitudes, and necessary as well as sufficient conditions for the existence of these solutions are also obtained.
基金supported by Science and Technology Project of Chongqing Municipal Education Committee (kJ110501) of ChinaNatural Science Foundation Project of CQ CSTC (cstc2012jjA20016) of ChinaNational Natural Science Foundation of China (11101298)
文摘In this article, the existence and uniqueness of positive solution for a class of nonlinear fractional differential equations is proved by constructing the upper and lower control functions of the nonlinear term without any monotone requirement. Our main method to the problem is the method of upper and lower solutions and Schauder fixed point theorem. Finally, we give an example to illuminate our results.
文摘Aim To investigate the existence of positive solutions for impulsive neutral differential equations. Methods The Banach contraction principle was used to establish our results. Results and Conclusion The results of the existence of positive solutions for impulsive neutral differential equations are obtained.
基金supported by the NNSF of China(10671064)the second author was supported by the Australian Research Council's Discovery Projects(DP0450752)
文摘This article considers the Dirichlet problem of homogeneous and inhomogeneous second-order ordinary differential systems. A nondegeneracy result is proven for positive solutions of homogeneous systems. Sufficient and necessary conditions for the existence of multiple positive solutions for inhomogeneous systems are obtained by making use of the nondegeneracy and uniqueness results of homogeneous systems.
基金Supported by the National Nature Science Foundation of China(11071001)Supported by the Key Program of Ministry of Education of China(205068)
文摘In this paper, we consider the positive solutions of fractional three-point boundary value problem of the form Dο^α＋u（t）＋f（t,u（t）,u＇（t）,…,u^（n-3）（5）,u^（n-2）（t））=0,u^（i）（0）=0,0≤i≤n-2,u^（n-2）（1）-βu^（n-2）（ξ）=0,where 0〈t〈1,n-1〈α≤n,n≥2,ξ Е（0,1）,βξ^a-n〈1. We first transform it into another equivalent boundary value problem. Then, we derive the Green＇s function for the equivalent boundary value problem and show that it satisfies certain properties. At last, by using some fixed-point theorems, we obtain the existence of positive solution for this problem. Example is given to illustrate the effectiveness of our result.
基金Supported by the Natural Science Foundation of Guangdong Province（032469）
文摘By utilizing a fixed point theorem on cone, some new results on the existence ofpositive periodic solutions for nonautonomous differential equations with delay are derived.
文摘In this paper, we investigate the existence of multiple positive periodic solutions for functional differential equations with infinite delay by applying the Krasnoselskii fixed point theorem for cone map and the Leggett-Williams fixed point theorem.
基金The research supported by the National Natural Science Foundation of China.
文摘This paper deals with the existence of positive periodic solutions for a kind of nonautonomous Volterra intergo-differential equations by employing the Krasnoselskii fixed point theorem. Applying the general theorems established to several biomathematical models, the paper improves some previous results and obtains some new results.
基金Supported by the National Natural Science Foundation of China,No.82473195 and No.32370797the Natural Science Foundation of Zhejiang Province,No.LTGY23H160018+3 种基金the Zhejiang Medical and Health Science and Technology Program,No.2024KY789 and No.2023KY615the National Research Center for Translational Medicine at Shanghai Program,No.NRCTM(SH)-2025-07the Beijing Science and Technology Innovation Medical Development Foundation,No.KC2023-JX-0270-07the Key Laboratory of Prevention,Diagnosis and Therapy of Upper Gastrointestinal Cancer of Zhejiang Province,No.2022E10021.
文摘BACKGROUND The log odds of positive lymph nodes(LODDS)are correlated with survival outcomes in gastric cancer(GC)patients.However,the prognostic value across different tumor differentiation levels remains unclear.AIM To evaluate the independent prognostic value of LODDS and the stratified predictive efficacy in GC patients with different histologic differentiations.METHODS We conducted a retrospective analysis of 2103 GC patients who underwent radical gastrectomy at Zhejiang Cancer Hospital.The prognostic value of LODDS was compared with that of other lymph node-based metrics,including the pathologic N stage,number of positive lymph nodes,number of total lymph nodes,and lymph node ratio,stratified by tumor differentiation.RESULTS LODDS was identified as an independent prognostic factor for overall survival in moderately to poorly differentiated GC patients.LODDS demonstrated superior predictive accuracy over other lymph node metrics.A nomogram incorporating LODDS,age,carbohydrate antigen(CA)125,carcinoembryonic antigen,and tumor differentiation showed good predictive accuracy(C-index=0.703).A higher LODDS was significantly associated with an increased risk of recurrence or metastasis,poorly differentiated tumors,advanced cancer,mucinous gastric adenocarcinoma,nerve invasion,and vascular tumor thrombus.Additionally,LODDS was positively correlated with the tumor markers CA19-9,CA72-4,CA125,and CA242(all P<0.05).CONCLUSION LODDS is an independent prognostic indicator for patients with moderately and poorly differentiated GC,and its predictive performance is superior to that of other models.
基金The University NSF (KJ2017A442,KJ2018A0452) of Anhui Provincial Education Departmentthe Foundation (2016XJGG13,2019XJZY02,2019XJSN03) of Suzhou University
文摘In this paper, we study a class of singular fractional differential system with Riemann-Stieltjes integral boundary condition by constructing a new cone and using Leggett-Williams fixed point theorem. The existence of multiple positive solutions is obtained. An example is presented to illustrate our main results.
基金The first author was supported by the Science Foundation of Educational Committee of HunanProvince ( 99C0 1 ) and the second author by the National Natural Science Foundation of China ( 1 9871 0 0 5 )
文摘The nonlinear differential equationx′(t)=-δ(t)x(t)+f(t,x(t))(*)is considered,where δ(t) is a periodic function of periodic T,f(t,x) is continuous and periodic in t.It is showed that (*) has at least two positive T-periodic solutions under certain growth conditions imposed on f.Applications will be presented to illustrate the main results.
基金High-End Foreign Expert Program Foundation from Chinese Foreign Experts Affairs,China(No.GDW20183300402)Characteristic College Foundation from Ningbo Education Bureau,China(No.TSXY-RCPY04-03)
文摘Sorting and collecting the data by questionnaire survey and literature analysis,the childrenswear brand elemental analysis is completed.The development goal of differentiated positioning of Chinese childrenswear brands is decided.Four modules which influence the brand differentiated development were extracted to establish the hierarchical analysis framework for the differentiated positioning development of Chinese childrenswear brand.Judgment matrix diagram is constructed by using the analytic hierarchy process(AHP).According to the data analysis and judgment,the core elements,basic elements and auxiliary elements are identified which support the development of differentiated positioning of Chinese childrenswear brands.The clear development path of differentiated positioning of Chinese childrenswear brands is formed,namely to enhance the core essential factors as the key point,to grasp the elements’spirit exactly in differentiated positioning of brand style,childrenswear color feature,green and security of products quality and retail prices which influence the brand differentiated development.The Chinese existing technical advantages was given full play by providing the basic support for the differentiated development of childrenswear brands.Auxiliary elements were heleped to grow by making auxiliary elements play a greater role.The goal was achieved to improve the market competitiveness by development of differentiated positioning of Chinese childrenswear brands.
文摘This paper is to obtain sufficient conditions under which the neutral functional differential equation d/dx[x(t) + integral(c)(t) x(s)d(s) mu(t, s)] + integral(c)(t) f(t, x(s))d(s) eta(t, s) = 0, t greater than or equal to t(0) greater than or equal to c (1) has a positive solution on [c, +infinity). Some results in [1] are generalized. Then we apply our results to functional differential equations of special form and obtain sufficient conditions for those equations to have a positive solution.
基金Supported by the Foundation for Outstanding Middle-Aged and Young Scientists of Shandong Province(Grant No.BS2010SF004)the National Natural Science Foundation of China(Grant No.10971179)+2 种基金a Project of Shandong Province Higher Educational Science and Technology Program(Grant Nos.J10LA53J11LA02)the Natural Science Foundation of Liaocheng University(Grant No.X09008)
文摘In this paper, existence of multiple positive solutions for fractional differential equations in Banach spaces is obtained by utilizing the fixed point index theory of completely continuous operators.
文摘This paper is to investigate the positive solutions of the systems of second-order ordinary differential equations with nonhomogeneous multi-point boundary conditions. By the lower and upper solutions method, Schauder fixed point theorem and fixed point index theory, under certain conditions, it is proved that there exist appropriate regions of parameters in which the problem has at least two, at least one or no positive solution.
