Nonlinear degenerate elliptic equation with Hardy potential and critical parameter

Some embedding inequalities in Hardy–Sobolev spaces with general weight functions were proved, and a positive answer to an open problem raised by Brezis–Vázquez was given. In the weighted Hardy–Sobolev spaces, the existence of nontrivial (many) solutions to the corresponding nonlinear degenerated elliptic equations with Hardy potential and critical parameter under conditions weaker than Ambrosetti–Rabinowitz condition, was obtained.