A GLOBAL COMPACTNESS RESULT FOR QUASILINEAR ELLIPTIC PROBLEMS WITH CRITICAL SOBOLEV NONLINEARITIES AND HARDY POTENTIALS ON RN

In this article, we study the elliptic equation with critical Sobolev nonlinearity and Hardy potentials (-triangle)p(u )+ a(x)|u|(p-1)u - mu | u | (p - 1) u / | x | p = | u |( p & lowast; - 2) u + f(x, u), u is an element of W-1,W-p(R-N), where 0 < <mu> < min{ ( N - p ) /p(p ) , N (p- 1) ( N - p 2 )/ p p } , p & lowast; = Np/ N-p is the critical Sobolev exponent. Through a compactness analysis of the associated functional operator, we obtain the existence of positive solutions under certain assumptions on a(x) and f(x, u).