On elliptic problems involving critical Hardy–Sobolev exponents and sign-changing function

Abstract

In this paper, we deal with the existence and nonexistence of nonnegative nontrivial weak solutions for a class of degenerate quasilinear elliptic problems with weights and nonlinearity involving the critical Hardy–Sobolev exponent and a sign-changing function. Some existence results are obtained by splitting the Nehari manifold and by exploring some properties of the best Hardy–Sobolev constant together with an approach developed by Brezis and Nirenberg.