Existence Of Solutions For Several Quasilinear Elliptic Equations

In this paper,we study the existence and multiplicity of weak solutions for two classes of quasilinear nonlocal elliptic boundary value problems.This paper is divided into four chapters as follows:The first chapter describes the background and current situation of research on quasilinear nonlocal elliptic boundary value problems,and gives the basic concepts and conclusions.In Chapter 2,by introducing a Nehari manifold and constructing a Fibering maps,it is proved that there are at least two weak solutions for the quasilinear Kirchhoff-type elliptic boundary value problem(?)where ? is the out region of a bounded region with smooth boundary in RN(N>1),1<p<N,??R1\{0} is a parameter,and the weight functions V(x),f(x)and g(x)satisfy certain conditions.In Chapter 3,we using the symmetric mountain pass Lemma of prove that there are infinite ly many weak solutions for the boundary value problem of nonlocal elliptic systems(?)when p=N,p*=?),?,?>0,??RN.We mainly use symmetric mountain pass lemma to prove the existence of the solution to this problem.In chapter 4,this paper is the summary of the whole thesis and the prospect of the future research.