The Existence And Multiple Solutions For Two Class Of Elliptic Partial Differential Equations Via Variational Method

In this master thesis,the existence and multiplicity of positive solutions for Schro-dinger equation with indefinite weight and the existence of ground state solution for a class of superlinear elliptic equation with p-Laplacian are considered by the variation-al methed.The main theorems are obtained by using the concentration-compactness lemma,the mountain pass theorem,Nehari method.The thesis contains five parts;The exordium is devoted to introducing previous results and recent progress.In the first chapter,we introduce some preliminaries which contain some impor-tant inequalities,definitions,some significant lemmas and theorems.In the second chapter,we study the existence and multiplicity of positive solutions to the following equation:(?)We proved the existence and multiplicity of positive solutions depend on the range of? when a(x),b(x),f(x)satisfy suitable conditions.In the third chapter,we study the existence of ground state solution to the fol-lowing superlinear elliptic equation with p-Laplacian(?) We proved there is a ground state solution at least when ? is contained in a right neighborhood of the first eigenvalue and the nonlinear term f(x,u)satisfies suitable assume.In the fourth chapter,we summarize the main works of this thesis and give some possible further studies.