Existence Of Solutions For Two Classes Of Elliptic Systems With Perturbation Terms

This thesis mainly studies the existence of solutions for two classes of elliptic system with perturbation terms.where ?,?>1 and satisfied ?+?<2^*:=????N?3?,h₁,h₂?H^-1?R^N?,h₁,n2?0 and h₁?0,h₂?0.·We solve the problem of the lack of compactness of the system?1?on the R^N by using the principle of compactness and use the mountain theorem to prove the existence of the solution of the system?1?.where s ????0,1?is fixed and?-??^s is the fractional Laplace operator,????R^N?N>2s?is a smooth bounded domain,h₁,h₂?L²???,q?x??L^????,q?x??0 a.e.in ?,and H?C¹?R²,R?is a homogeneous function of degree p with 2<p<2_s^*:=???.We prove the existence of the solution of the system?2?by the Nehari manifold and the variational method.This thesis is divided into three chapters.In the first chapter,we first introduce some research status of the current elliptic system,and then introduce the main results of this paper.In the second chapter,the existence of solutions for semilinear elliptic system?1?with perturbation terms on unbounded regions is discussedIn the third chapter,the existence of solutions of fractional order elliptic system?2?with perturbation terms on bounded regions is studied.