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

This paper discusses the existence of multiple high-energy solutions for a p$$ p $$-Laplacian system involving critical Hardy-Sobolev nonlinearity in Double-struck capital RN$$ {\mathrm{\mathbb{R}}} circumflex N $$. Considering that the "double" lack of compactness in the system is caused by the unboundedness of Double-struck capital RN$$ {\mathrm{\mathbb{R}}} circumflex N $$ and the presence of the critical Hardy-Sobolev exponent, we demonstrate the version to Double-struck capital RN$$ {\mathrm{\mathbb{R}}} circumflex N $$ of Struwe's classical global compactness result for double p$$ p $$-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.