Nehari流形在一个拟线性方程组中的应用

主要研究带有非齐次边界条件的拟线性椭圆方程组的正解问题,在合适参数条件下,用变分方法和流形方法得到该椭圆方程组正解的存在性和多解性.结论推广了近期发表的结果.     

一类周期非线性差分方程的基态解

本文研究了一类二阶周期非线性差分方程基态解的存在性问题.利用临界点理论结合Nehari流形方法,获得了此类方程基态解的存在性.在比经典AR条件更一般的超二次条件下,本文结论推广了已有的结果,并举例说明此类方程解的存在性.     

Ground state solutions for an indefinite Kirchhoff type problem with steep potential well

In this paper we study an indefinite Kirchhoff type equation with steep potential well. Under some suitable conditions, the existence and the non-existence of nontrivial solutions are obtained by using variational methods. Furthermore, the phenomenon of concentration of solutions is also explored.     

Multiplicity of nodal solutions for elliptic problems involving non-odd nonlinearities

In this paper, we study the effect of domain shape on the number of 2-nodal solutions for the semilinear elliptic equation involving non-odd nonlinearities. We prove that a semilinear elliptic equation in an m$m$-bump domain (possibly unbounded) has m²$m^2$ 2-nodal solutions and we can find a least energy nodal solution in those solutions. Furthermore, we can describe the bump location of these solutions.     

Boundary-value Problems for Integro-differential Equations of Elliptic Type

In this paper we study the existence of solutions to the Dirichlet problem for a class of integro-differential equations of elliptic type by using the weakly continuous method.     

Existence and multiplicity of nodal solutions for Dirichlet problems in upper half strip with holes

In this paper, we consider the existence and multiplicity of nodal solutions of semilinear elliptic equations. We prove that a semilinear elliptic equation in large domains does not admit any least energy nodal (sign-changing) solution and in an upper half strip with m-holes has at least m² 2-nodal solutions.     

ON GROUND STATE SOLUTIONS FOR SUPERLINEAR DIRAC EQUATION

This article is concerned with the nonlinear Dirac equations-iatψ = ich3Σk=1αkakψ- mc2βψ + Rψ(x, ψ) in R3.Under suitable assumptions on the nonlinearity, we establish the existence of ground state solutions by the generalized Nehari manifold method developed recently by Szulkin and Weth.     

Existence of multiple positive solutions for semilinear elliptic systems involving m critical hardy-sobolev exponents and m sign-changing weight function

In this article, we consider a class of degenerate quasilinear elliptic problems with weights and nonlinearity involving the critical Hardy-Sobolev exponent and one sign-changing function. The existence and multiplicity results of positive solutions are obtained by variational methods.     

Four 2-nodal solutions for a semilinear elliptic equation in a finite strip with a hole

In this paper, we study the decomposition of the filtration of the Nehari manifold via the variation of domain shape. We use this result to prove that the semilinear elliptic equation in a finite strip with hole has at least four 2-nodal solutions (solutions with precisely two nodal domains). Furthermore, we can describe the bump location of these solutions.