EXISTENCE RESULTS TO SOME QUASILINEAR ELLIPTIC PROBLEMS WITH HARDY POTENTIAL AND ABSORPTION TERM

Abstract

This article is devoted to dealing with existence of a solution to a quasilinear elliptic problem with the Hardy potential term u^p−1 / |x|^p and critical growth in the gradient |∇u|^p as an absorption term. By considering the interaction between the two terms in the equation, we prove that there exists a positive solution to the problem. Moreover, the existence result for a wider class of weight functions can also be obtained.