The Existence Of Nontrivial Solutions For A Class Of Elliptic Equations Of Schr(?)dinger Type

In the paper, we study the existence of nontrivial solutions for a class of elliptic equations of schr?dinger type. Through the variable transformation, the quasilinear equation is converted into a semilinear one with some relevant conditions. Meanwhile, we convert this problem of the existence of nontrivial solutions for the partial differential equations to the existence of nontrivial critical point of the energy functional corresponding to the partial differential equation mainly through the variational method. Then we study the existence of nontrivial solutions fo r the equation by using some mathematical theories such as mountain pass lemma, Palais-Smale condition, Cerami condition and Lions lemma.In the first chapter, the research background and the main content of this article are briefly introduced. We also introduce some basic knowledge which is applied in the article. And we introduce the main content of this article.In the second chapter, we are concerned with the existence of nontrivial solution o f the following Schr?dinger equation where k＜0, N≥3,α＞1. Using variational method, mountain pass lemma, Lions lemma and Palais-Smale condition, we can prove the existence of the nontrivial solutions for the partial differential equations without(AR) condition.In the third chapter, we study the existence of nontrivial solutions of the following equation Where k≥0, N≥3,α＞1, q∈(2, 2~*), we can prove the existence of the nontrivial solution by using variational method, mountain pass lemma and cerami condition.