Approximate Weak Minimal Solutions of Set-Valued Optimization Problems

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.

On the Minimal Solutions of Variational Inequalities in Orlicz-Sobolev Spaces

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.

EXISTENCE OF SOLUTIONS FOR PERIODIC BOUNDARY VALUE PROBLEMS FOR SECOND-ORDER INTEGRO-DIFFERENTIAL EQUATIONS

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.

ANISOTROPIC(p,q)-EQUATIONS WITH COMPETITION PHENOMENA

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.

Solutions of Minimal Period for An Extended Hamiltonian System

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.

L^p(p > 1) Solutions of BSDEs with Generators Satisfying Some Non-uniform Conditions in t and ω

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.

Blow-up Dynamics of L^2 Solutions for the Davey–Stewartson System

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.

Transition-layer Solutions of Quasilinear Elliptic Boundary Blow-up Problems and Dirichlet Problems

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.

PERIODIC BOUNDARY VALUE PROBLEMS FOR DIFFERENTIAL EQUATIONS WITH “SUPREMUM”

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.

Convergence of Monotone Iterations for Differential Problem

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.