Study On Two Elliptic Systems Involving Different Hardy Terms And Strongly Coupled Critical Terms

In this paper,we study the asymptotic properties of a class of elliptic equations with different Hardy terms and strongly coupled critical terms.The existence of Mountain-pass solutions for equations with subcritical perturbations are proved by the variational method.This paper is divided into three chapters:The first chapter mainly introduces the research problems in this paper and the background of the system of equations.Secondly,we give the symbols and related preparatory knowledge that need to be used in this article.Finally,the research result and the corresponding structure are given.In Chapter 2,we mainly study the asymptotic properties of radially-symmetric and strictly-decreasing solutions to a system of equations in?~N.The asymptotic property at the origin and infinity of the radially-symmetric and strictly-decreasing solutions for equations are established by means of the analysis method of ODEs.In addition,the asymptotic property of the radial and decreasing minimizers to the best Sobolev constant are established.In Chapter 3,we mainly discuss the existence of Mountain-pass solutions for equations with subcritical perturbations.Firstly,the local Palais-Smale condition is established.Secondly,the truncation estimation technique is fully used to truncate the extremal function corresponding to the best Sobolev constant.Finally,the existence of the Mountain-pass solutions are proved by the variational method.