Research On Solutions Of Critical Elliptic Systems With P-Laplacian Operator And Multiple Strongly Coupled Hardy Terms And Multiple Singular Points

A class of critical elliptic systems with p-Laplacian operator,multiple strongly coupled Hardy terms and multiple singularities are studied by variational methods,analytical techniques,and truncated functions on the whole space and bounded domains.In chapter 1,the problems studied in this article are briefly introduced,some helpful references for this article are listed,the definitions and conditions that need to be used are explained,and the conclusions and theorems obtained from the research are summarized.In chapter 2,the existence and nonexistence of ground state solutions for a class of systems(1.1.2)in the whole space are studied.First of all,the local (PS)_c conditions that the energy functional J corresponding to the elliptic systems(1.1.1)in the whole space meet under certain conditions are discussed.Secondly,under the assumptions,the asymptotic estimation result of the extreme value function of the relevant best Sobolev constant is obtained,and the relationship between the relevant best Sobolev constant is clarified,and the existence of the ground state solution of the elliptic systems(1.1.1)is clarified by the variational method.And under another hypothetical condition,the infimum of the relevant best Sobolev constant cannot be reached has also been proved,and the non-existence of the ground state solution of the elliptic systems(1.1.1)under this hypothetical condition is also confirmed by the method of contradiction.In chapter 3,the ground state solutions of a class of systems(1.1.2)in bounded domains is studied.First,the local (PS)_c condition that the energy functional J_? corresponding to the elliptic equations(1.1.2)in the bounded domain meets certain conditions is proved.And the relationship between the relevant best Sobolev constants is confirmed by the truncation function and analytical techniques.The existence of the ground state solution of the elliptic systems(1.1.2)under the assumptions is also proved.