In this paper,we consider the fourth-order parabolic equation with p(x)Laplacian and variable exponent source ut+∆^(2)u−div(|■u|^(p(x)−2■u))=|u|^(q(x))−1u.By applying potential well method,we obtain global existence...In this paper,we consider the fourth-order parabolic equation with p(x)Laplacian and variable exponent source ut+∆^(2)u−div(|■u|^(p(x)−2■u))=|u|^(q(x))−1u.By applying potential well method,we obtain global existence,asymptotic behavior and blow-up of solutions with initial energy J(u_(0))≤d.Moreover,we estimate the upper bound of the blow-up time for J(u_(0))≤0.展开更多
In this paper,we study the weighted higher order semilinear equation in an exterior domain(-△)^(m)u=|x|^(α)g(u)in R^(N)\B_(R_(0)),where N≥1,m≥2 are integers,α>-2m,g is a continuous and nondecreasing function i...In this paper,we study the weighted higher order semilinear equation in an exterior domain(-△)^(m)u=|x|^(α)g(u)in R^(N)\B_(R_(0)),where N≥1,m≥2 are integers,α>-2m,g is a continuous and nondecreasing function in(0,+∞)and positive in(0,+∞),B_(R_(0))is the ball of the radius R0 centered at the origin.We prove that a positive supersolution of the problem which verifies(-△)_(i)u>0 in R^(N)\B_(R_(0))(i=0,…,m-1)exists if and only if N>2m and∫_(0)^(δ)g(t)/t^(2(N-m)+α/N-2m)dt<∞,,for someδ>0.We further obtain some existence and nonexistence results for the positive solution to the Dirichlet problem when g(u)=u^(p)with p>1,by using the Pohozaev identity and an embedding lemma of radial Sobolev spaces.展开更多
We investigate the long time existence of strong solutions to the initial value problem for the three-dimensional non-isentropic compressible Navier-Stokes-Korteweg system.Under the conditions of slight density and te...We investigate the long time existence of strong solutions to the initial value problem for the three-dimensional non-isentropic compressible Navier-Stokes-Korteweg system.Under the conditions of slight density and temperature variations,we verify that the full compressible Navier-Stokes-Korteweg equations admit a unique strong solution as long as the solution of the limiting system exists,when the Mach number is sufficiently small.Furthermore,we deduce the uniform convergence of strong solutions for the compressible system toward those for the corresponding incompressible system on the time interval in which the solution exists.展开更多
In this paper,a class of quaternion-valued cellular neural networks(QVCNNS)with time-varying delays are considered.Combining graph theory with the continuation theorem of Mawhin’s coincidence degree theory as well as...In this paper,a class of quaternion-valued cellular neural networks(QVCNNS)with time-varying delays are considered.Combining graph theory with the continuation theorem of Mawhin’s coincidence degree theory as well as Lyapunov functional method,we establish new criteria on the existence and exponential stability of periodic solutions for QVCNNS by removing the assumptions for the boundedness on the activation functions and the assumptions that the values of the activation functions are zero at origin.Hence,our results are less conservative and new.展开更多
In this paper, some sufficient conditions on the existence of non-trivial periodic solutions of the system dx/dt=e(y), dy/dt=- f(x)h(y)- g(x)are obtained, which not only generalize some known results concerning the Li...In this paper, some sufficient conditions on the existence of non-trivial periodic solutions of the system dx/dt=e(y), dy/dt=- f(x)h(y)- g(x)are obtained, which not only generalize some known results concerning the Lienard system in this direction, but also relax or eliminate some traditional assumptions.展开更多
托马斯.阿奎那的形而上学是以是(being)为中心、以本质(essence)和存在(existence)的关系学说为枢纽的存在论。阿奎那认为,形而上学或存在论所探讨的特殊的固有对象即是是(to on,esse,being)自身,或者称之为是之所以为是(esse in quantu...托马斯.阿奎那的形而上学是以是(being)为中心、以本质(essence)和存在(existence)的关系学说为枢纽的存在论。阿奎那认为,形而上学或存在论所探讨的特殊的固有对象即是是(to on,esse,being)自身,或者称之为是之所以为是(esse in quantum esse,being as beinginjeneral)。他在论证是自身时强调实在意义上的是重于逻辑意义的是。是(being)包括本质(essence)与存在(existence);本质(essence)与存在(existence)皆为是者(beings)。而存在(existence)先于本质(essence);存在(existence)是是(being)之最具体的、个别的、实体的、独一无二的完美实现(act)。托马斯.阿奎那的存在论哲学颠覆了传统哲学中存在与本质的位置,它以一种存在主义代替本质主义,从而在形而上学历史上掀起一场革命。展开更多
The philosophical root of all human beings’ existence crisis in the contemporary times is the philosophy of the unlimited theory. The inner spiritual supporting force is the construction from its theoretical reason t...The philosophical root of all human beings’ existence crisis in the contemporary times is the philosophy of the unlimited theory. The inner spiritual supporting force is the construction from its theoretical reason to its scientific reason. Its essential ideas stem from the people-centered theory, the view of happiness in the material- purposed theory, the communist life style, the material hegemonist principle, and the rational action principles of economic technology. In the 21st century, in order to deal with the dangerous situation of human beings’ exist- ence from the root, the philosophy of the limitation theory must be established, which has the eco-reason as the value support, integrates all the original wisdom of human beings and reflects human’s spiritual needs of the age as well as the direction of human future development. The whole percept of this new philosophy is that “all things have souls”; its basic law of existence is “the ceaseless life circle”; its survival goal is the view of happiness in the harmony of material and spirit; its social action guidance and principle are (environment, society, humanity) the environment ecologism and the integral-and-mutual action principle (of human beings &society, individual &society, and present age & posterity).展开更多
Aim The existence of generalized solution for a class of nonlinear partial differential equations with nonhanogeneous boundary condition was investigated. This problem arises from polymer processing concerned with the...Aim The existence of generalized solution for a class of nonlinear partial differential equations with nonhanogeneous boundary condition was investigated. This problem arises from polymer processing concerned with the first initial-boundary value problem or the nonstationary floW of non-Newtonian viscous incompressiblee fluid through the slit dice. MethodsThe monotone operator theory and the Schauder's fixal point theorem were used. Results and Conclusion The existence theorem of generalized solutions for a the of nonlinear partial differential equations with nonhormogeneous boundary condition is proved under reasonable conditions展开更多
In this paper we investigate the existence of positive solution for a class of fourth_order superlinear semipositone eigenvalue problems. This class of problems usually describes the deformation of the elastic beam wh...In this paper we investigate the existence of positive solution for a class of fourth_order superlinear semipositone eigenvalue problems. This class of problems usually describes the deformation of the elastic beam whose both end_points are fixed.展开更多
基金Supported by NSFC(No.12101482)the Natural Science Foundation of Shaanxi Province,China(No.2018JQ1052)。
文摘In this paper,we consider the fourth-order parabolic equation with p(x)Laplacian and variable exponent source ut+∆^(2)u−div(|■u|^(p(x)−2■u))=|u|^(q(x))−1u.By applying potential well method,we obtain global existence,asymptotic behavior and blow-up of solutions with initial energy J(u_(0))≤d.Moreover,we estimate the upper bound of the blow-up time for J(u_(0))≤0.
文摘In this paper,we study the weighted higher order semilinear equation in an exterior domain(-△)^(m)u=|x|^(α)g(u)in R^(N)\B_(R_(0)),where N≥1,m≥2 are integers,α>-2m,g is a continuous and nondecreasing function in(0,+∞)and positive in(0,+∞),B_(R_(0))is the ball of the radius R0 centered at the origin.We prove that a positive supersolution of the problem which verifies(-△)_(i)u>0 in R^(N)\B_(R_(0))(i=0,…,m-1)exists if and only if N>2m and∫_(0)^(δ)g(t)/t^(2(N-m)+α/N-2m)dt<∞,,for someδ>0.We further obtain some existence and nonexistence results for the positive solution to the Dirichlet problem when g(u)=u^(p)with p>1,by using the Pohozaev identity and an embedding lemma of radial Sobolev spaces.
文摘We investigate the long time existence of strong solutions to the initial value problem for the three-dimensional non-isentropic compressible Navier-Stokes-Korteweg system.Under the conditions of slight density and temperature variations,we verify that the full compressible Navier-Stokes-Korteweg equations admit a unique strong solution as long as the solution of the limiting system exists,when the Mach number is sufficiently small.Furthermore,we deduce the uniform convergence of strong solutions for the compressible system toward those for the corresponding incompressible system on the time interval in which the solution exists.
基金Supported by the Innovation Platform Open Fund in Hunan Province Colleges and Universities of China(201485).
文摘In this paper,a class of quaternion-valued cellular neural networks(QVCNNS)with time-varying delays are considered.Combining graph theory with the continuation theorem of Mawhin’s coincidence degree theory as well as Lyapunov functional method,we establish new criteria on the existence and exponential stability of periodic solutions for QVCNNS by removing the assumptions for the boundedness on the activation functions and the assumptions that the values of the activation functions are zero at origin.Hence,our results are less conservative and new.
文摘In this paper, some sufficient conditions on the existence of non-trivial periodic solutions of the system dx/dt=e(y), dy/dt=- f(x)h(y)- g(x)are obtained, which not only generalize some known results concerning the Lienard system in this direction, but also relax or eliminate some traditional assumptions.
文摘托马斯.阿奎那的形而上学是以是(being)为中心、以本质(essence)和存在(existence)的关系学说为枢纽的存在论。阿奎那认为,形而上学或存在论所探讨的特殊的固有对象即是是(to on,esse,being)自身,或者称之为是之所以为是(esse in quantum esse,being as beinginjeneral)。他在论证是自身时强调实在意义上的是重于逻辑意义的是。是(being)包括本质(essence)与存在(existence);本质(essence)与存在(existence)皆为是者(beings)。而存在(existence)先于本质(essence);存在(existence)是是(being)之最具体的、个别的、实体的、独一无二的完美实现(act)。托马斯.阿奎那的存在论哲学颠覆了传统哲学中存在与本质的位置,它以一种存在主义代替本质主义,从而在形而上学历史上掀起一场革命。
文摘The philosophical root of all human beings’ existence crisis in the contemporary times is the philosophy of the unlimited theory. The inner spiritual supporting force is the construction from its theoretical reason to its scientific reason. Its essential ideas stem from the people-centered theory, the view of happiness in the material- purposed theory, the communist life style, the material hegemonist principle, and the rational action principles of economic technology. In the 21st century, in order to deal with the dangerous situation of human beings’ exist- ence from the root, the philosophy of the limitation theory must be established, which has the eco-reason as the value support, integrates all the original wisdom of human beings and reflects human’s spiritual needs of the age as well as the direction of human future development. The whole percept of this new philosophy is that “all things have souls”; its basic law of existence is “the ceaseless life circle”; its survival goal is the view of happiness in the harmony of material and spirit; its social action guidance and principle are (environment, society, humanity) the environment ecologism and the integral-and-mutual action principle (of human beings &society, individual &society, and present age & posterity).
文摘Aim The existence of generalized solution for a class of nonlinear partial differential equations with nonhanogeneous boundary condition was investigated. This problem arises from polymer processing concerned with the first initial-boundary value problem or the nonstationary floW of non-Newtonian viscous incompressiblee fluid through the slit dice. MethodsThe monotone operator theory and the Schauder's fixal point theorem were used. Results and Conclusion The existence theorem of generalized solutions for a the of nonlinear partial differential equations with nonhormogeneous boundary condition is proved under reasonable conditions
文摘In this paper we investigate the existence of positive solution for a class of fourth_order superlinear semipositone eigenvalue problems. This class of problems usually describes the deformation of the elastic beam whose both end_points are fixed.
