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 ℝN$$ {\mathrm{\mathbb{R}}}^N $$. Considering that the "double" lack of compactness in the system is caused by the unboundedness of ℝN$$ {\mathrm{\mathbb{R}}}^N $$ and the presence of the critical Hardy–Sobolev exponent, we demonstrate the version to ℝN$$ {\mathrm{\mathbb{R}}}^N $$ 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. [ABSTRACT FROM AUTHOR]