On The Solutions Of Critical Elliptic Systems Involving Multiple Strongly-coupled Hardy Terms

In this paper,the related properties of solutions to a critical elliptic system involving multiple strong-coupled Hardy-type terms is studied.And the discussion is divided into four chapters.In the first chapter,the research background of this paper is given,including symbols,definitions and main conclusions used in this paper,and finally briefly explains the main structure of the thesis.In Chapter 2,the convergence of minimization sequences is studied by using the concentration-compactness principle and Schwartz symmetrization method,as a result,the existence of ground state solutions of elliptic equations is further proved.In Chapter 3,we study the radially-symmetric and strictly-decreasing solutions of elliptic equations,which involves multiple strongly-coupled Hardy-type terms and critical nonlinearities.By the ODEs analysis methods,the asymptotic behaviors at the origin and infinity of solutions are proved.It is found that the singularities of u and v in the solution(u,v)are at the same level.Finally,in Chapter 4,the existence of explicit form of least energy solutions is proved under certain assumptions,among which explicit ground state solution to the system is found.