On Elliptic Problems Involving Critical Hardy-Sobolev Exponents and Sign-Changing Function

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 thecritical Hardy-Sobolev exponent and a sign-changing function. Some existence results are obtained by splitting the Nerahi manifold and by exploring some properties of the best Hardy-Sobolev constanttogether with an approach developed by Brezis and Nirenberg.