Global compactness results for quasilinear elliptic problems with combined critical Sobolev–Hardy terms ☆

Abstract In this paper, we study the global compactness results for quasilinear elliptic problems involving combined critical Sobolev–Hardy terms on the whole space and a bounded smooth domain, respectively. That is, we give the complete descriptions for the Palais–Smale (PS) sequences of the corresponding energy functionals. By using these descriptions, the existence results of solutions are also obtained.