Multiple high‐energy solutions for an elliptic system with critical Hardy–Sobolev nonlinearity

Abstract

This paper discusses the existence of multiple high‐energy solutions for a ‐Laplacian system involving critical Hardy‐Sobolev nonlinearity in . Considering that the “double” lack of compactness in the system is caused by the unboundedness of and the presence of the critical Hardy–Sobolev exponent, we demonstrate the version to of Struwe's classical global compactness result for double ‐Laplace operator. In virtue of the quantitative deformation lemma, a barycenter function, and the Brouwer degree theory, the existence of multiple high‐energy solutions is established. The results of this paper extend and complement the recent work.