Research On High-dimensional Cloth Point Solutions Of Several Types Of Elliptic Problem

In this paper,we study the existence of infinite solutions of several nonlinear elliptic equations by Lyapunov-Schmidt reduction method.The paper is divided into three chapters:In chapter one,we mainly describe the background and research status of the problems discussed in this paper,and briefly introduce the main work.In chapter two,we study the existence of positive solutions of the nonlinear fractional Schr(?)dinger equation(-Δ)su+V(x)u=up,u>0,x∈RN,u∈Hs(RN),where s ∈(0,1),p∈(1,2s*-1),2s*=2N/N-2s.we prove that there are infinitely many non-radially symmetric positive solutions of the equation,and their energy functional can be arbitrarily large.In chapter three,we discuss the existence of the positive solution of fractional critical elliptic equation(-Δ)su=K(|y|/μ)u2s*-1,u>0,u∈Ds(RN),when K(x)decaying conditions are satisfied,we prove that there are infinitely many non-radially symmetric positive solutions of the equation,and their energy functional can be arbitrarily large.