Liouville Theorem Of Semilinear Elliptic Equation And The Fractional Laplacians With Partial Hardy Term Double Critical Elliptic Problem

In this thesis, we investigate the Morse index and weighted type Liouville theorem of elliptic equation and the fractional Laplacians with partial Hardy term double critical elliptic problem. This thesis is divided into three chapters.In chapter 1, we introduce the background of the problem and main results of the thesis.In chapter 2, we study the Liouville theorem for weighted semilinear elliptic equations and Where N≥ 3 and α>-2. we prove that the bounded solutions of the above problems with finite Morse indices are zero when 1< p< （N+2α+2）/（N-2）.In chapter 3, We are devoted to the study of the existence of nontrivial solution for the following critical problem with partial Hardy term on R^N where is the a-fractional critical sobolev exponent, and γ<γH（N, K, α）= D_N,K,αC_N,α,the latter being the fractional partial Hardy constant on R^N.