This paper deals with approximate weak minimal solutions of set-valued optimization problems under vector and set optimality criteria.The relationships between various concepts of approximate weak minimal solutions ar...This paper deals with approximate weak minimal solutions of set-valued optimization problems under vector and set optimality criteria.The relationships between various concepts of approximate weak minimal solutions are investigated.Some topological properties and existence theorems of these solutions are given.It is shown that for set-valued optimization problems with upper(outer)cone-semicontinuous objective values or closed objective maps the approximate weak minimal and strictly approximate lower weak minimal solution sets are closed.By using the polar cone and two scalarization processes,some necessary and sufficient optimality conditions in the sense of vector and set criteria are provided.展开更多
In this paper,the author studies the existence of the minimal nonnegative solutions of some elliptic variational inequalities in Orlicz-Sobolev spaces on bounded or unbounded domains.She gets some comparison results b...In this paper,the author studies the existence of the minimal nonnegative solutions of some elliptic variational inequalities in Orlicz-Sobolev spaces on bounded or unbounded domains.She gets some comparison results between different solutions as tools to pass to the limit in the problems and to show the existence of the minimal solutions of the variational inequalities on bounded domains or unbounded domains.In both cases,coercive and noncoercive operators are handled.The sufficient and necessary conditions for the existence of the minimal nonnegative solution of the noncoercive variational inequality on bounded domains are established.展开更多
By establishing a comparison result and using monotone iterative methods, the theorem of existence for minimal and maximal solutions of periodic boundary value problems for second-order nonlinear integro-differential ...By establishing a comparison result and using monotone iterative methods, the theorem of existence for minimal and maximal solutions of periodic boundary value problems for second-order nonlinear integro-differential equations in Banach spaces is proved.展开更多
We consider a nonlinear Robin problem driven by the anisotropic(p,q)-Laplacian and with a reaction exhibiting the competing effects of a parametric sublinear(concave) term and of a superlinear(convex) term.We prove a ...We consider a nonlinear Robin problem driven by the anisotropic(p,q)-Laplacian and with a reaction exhibiting the competing effects of a parametric sublinear(concave) term and of a superlinear(convex) term.We prove a bifurcation-type theorem describing the changes in the set of positive solutions as the parameter varies.We also prove the existence of a minimal positive solution and determine the monotonicity and continuity properties of the minimal solution map.展开更多
Solutions of minimal period for the Hamiltonian system =JH′(x) has been proven under the conditionas H″(x) -1 →0 as |x|→∞ and H(x) is of higher order than 2 in the neighborhood of the origin; In this paper, w...Solutions of minimal period for the Hamiltonian system =JH′(x) has been proven under the conditionas H″(x) -1 →0 as |x|→∞ and H(x) is of higher order than 2 in the neighborhood of the origin; In this paper, we extend the result to the problem J=H^′(x)+Qx with Q symmetric and H^ (x) satisfying the same assumption.展开更多
This paper is devoted to the L^p(p > 1) solutions of one-dimensional backward stochastic differential equations(BSDEs for short) with general time intervals and generators satisfying some non-uniform conditions in ...This paper is devoted to the L^p(p > 1) solutions of one-dimensional backward stochastic differential equations(BSDEs for short) with general time intervals and generators satisfying some non-uniform conditions in t and ω. An existence and uniqueness result,a comparison theorem and an existence result for the minimal solutions are respectively obtained, which considerably improve some known works. Some classical techniques used to deal with the existence and uniqueness of L^p(p > 1) solutions of BSDEs with Lipschitz or linear-growth generators are also developed in this paper.展开更多
We study the blow-up solutions for the Davey-Stewartson system(D-S system, for short)in L2x(R2). First, we give the nonlinear profile decomposition of solutions for the D-S system. Then, we prove the existence of ...We study the blow-up solutions for the Davey-Stewartson system(D-S system, for short)in L2x(R2). First, we give the nonlinear profile decomposition of solutions for the D-S system. Then, we prove the existence of minimal mass blow-up solutions. Finally, by using the characteristic of minimal mass blow-up solutions, we obtain the limiting profile and a precisely mass concentration of L2 blow-up solutions for the D-S system.展开更多
We study profiles of positive solutions for quasilinear elliptic boundary blow-up problems and Dirichlet problems with the same equation:where ω 〉 0, a(x) is a continuous function satisfying 0 〈 a(x) 〈 1 for...We study profiles of positive solutions for quasilinear elliptic boundary blow-up problems and Dirichlet problems with the same equation:where ω 〉 0, a(x) is a continuous function satisfying 0 〈 a(x) 〈 1 for x ∈Ω, Ω is a bounded smooth domain in R^N. We will see that the profile of a minimal positive boundary blow-up solution of the equation shares some similarities to the profile of a positive minimizer solution of the equation with homogeneous Dirichlet boundary condition.展开更多
In this paper, the monotone iterative method of Lakshmikantham and a comparison result are applied to study a periodic boundary value problem for a nonlinear impulsive differential equation with 'supremum' and...In this paper, the monotone iterative method of Lakshmikantham and a comparison result are applied to study a periodic boundary value problem for a nonlinear impulsive differential equation with 'supremum' and the existence of maximal and minimal solutions are obtained.展开更多
We use the method of lower and upper solutions combined with monotone iterations to differential problems with a parameter. Existence of extremal solutions to such problems is proved.
基金Institute for Research in Fundamental Sciences(No.96580048).
文摘This paper deals with approximate weak minimal solutions of set-valued optimization problems under vector and set optimality criteria.The relationships between various concepts of approximate weak minimal solutions are investigated.Some topological properties and existence theorems of these solutions are given.It is shown that for set-valued optimization problems with upper(outer)cone-semicontinuous objective values or closed objective maps the approximate weak minimal and strictly approximate lower weak minimal solution sets are closed.By using the polar cone and two scalarization processes,some necessary and sufficient optimality conditions in the sense of vector and set criteria are provided.
基金supported by the 100 Teachers Database Project of Shanghai University of Medicine and Health Sciences(No.B30200203110084)。
文摘In this paper,the author studies the existence of the minimal nonnegative solutions of some elliptic variational inequalities in Orlicz-Sobolev spaces on bounded or unbounded domains.She gets some comparison results between different solutions as tools to pass to the limit in the problems and to show the existence of the minimal solutions of the variational inequalities on bounded domains or unbounded domains.In both cases,coercive and noncoercive operators are handled.The sufficient and necessary conditions for the existence of the minimal nonnegative solution of the noncoercive variational inequality on bounded domains are established.
基金theNaturalScienceFoundationofEducationalCommitteeofHainanProvince China
文摘By establishing a comparison result and using monotone iterative methods, the theorem of existence for minimal and maximal solutions of periodic boundary value problems for second-order nonlinear integro-differential equations in Banach spaces is proved.
基金supported by NNSF of China(12071413)NSF of Guangxi(2018GXNSFDA138002)。
文摘We consider a nonlinear Robin problem driven by the anisotropic(p,q)-Laplacian and with a reaction exhibiting the competing effects of a parametric sublinear(concave) term and of a superlinear(convex) term.We prove a bifurcation-type theorem describing the changes in the set of positive solutions as the parameter varies.We also prove the existence of a minimal positive solution and determine the monotonicity and continuity properties of the minimal solution map.
文摘Solutions of minimal period for the Hamiltonian system =JH′(x) has been proven under the conditionas H″(x) -1 →0 as |x|→∞ and H(x) is of higher order than 2 in the neighborhood of the origin; In this paper, we extend the result to the problem J=H^′(x)+Qx with Q symmetric and H^ (x) satisfying the same assumption.
基金supported by the Fundamental Research Funds for the Central Universities(No.2017XKQY98)。
文摘This paper is devoted to the L^p(p > 1) solutions of one-dimensional backward stochastic differential equations(BSDEs for short) with general time intervals and generators satisfying some non-uniform conditions in t and ω. An existence and uniqueness result,a comparison theorem and an existence result for the minimal solutions are respectively obtained, which considerably improve some known works. Some classical techniques used to deal with the existence and uniqueness of L^p(p > 1) solutions of BSDEs with Lipschitz or linear-growth generators are also developed in this paper.
基金Supported by National Natural Science Foundation of China(Grant No.11371267)Research Fund for the Doctoral Program of Higher Education of China(Grant No.20125134120001)
文摘We study the blow-up solutions for the Davey-Stewartson system(D-S system, for short)in L2x(R2). First, we give the nonlinear profile decomposition of solutions for the D-S system. Then, we prove the existence of minimal mass blow-up solutions. Finally, by using the characteristic of minimal mass blow-up solutions, we obtain the limiting profile and a precisely mass concentration of L2 blow-up solutions for the D-S system.
基金Supported by National Natural Science Foundation of China (Grant No. 10871060)
文摘We study profiles of positive solutions for quasilinear elliptic boundary blow-up problems and Dirichlet problems with the same equation:where ω 〉 0, a(x) is a continuous function satisfying 0 〈 a(x) 〈 1 for x ∈Ω, Ω is a bounded smooth domain in R^N. We will see that the profile of a minimal positive boundary blow-up solution of the equation shares some similarities to the profile of a positive minimizer solution of the equation with homogeneous Dirichlet boundary condition.
基金Research supported by the foundation of Educational Department of Fujian Province (K200ll04)and Zhangzhou Teachers College.
文摘In this paper, the monotone iterative method of Lakshmikantham and a comparison result are applied to study a periodic boundary value problem for a nonlinear impulsive differential equation with 'supremum' and the existence of maximal and minimal solutions are obtained.
文摘We use the method of lower and upper solutions combined with monotone iterations to differential problems with a parameter. Existence of extremal solutions to such problems is proved.