Liouville Theorems For Stable Solutions Of The Weighted Lane-Emden System

In this dissertation,we study the nonexistence of positive stable solutions of a class of weighted Lane-Emden system Where ?(?)RN,0<p<1<p-1<? and ? is a continuous function with 0<p(x)<C.We study the following two cases:Case 1:When the domain is a bounded region,the weighted Lane-Emden system is equivalent to the weighted m-biharmonic equations,and the problem of nonexistence of positive stable solutions of the equation in bounded domain is solved.Case 2:When the domain is an out-of-compact set region and(x·??)? 0,simultaneously,by using the elliptic theorems and Pohozaev equation,the nonexistence of positive stable solutions for the system outside the compact set is established,and the nonexistence of positive stable solutions for the weighted biharmonic equation outside the compact set is further proved.