Nonlinear elliptic systems involving Hardy-Sobolev Criticalities

Rafael López-Soriano; Alejandro Ortega

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arXiv · 2211.17047

Nonlinear elliptic systems involving Hardy-Sobolev Criticalities

Rafael López-Soriano·Alejandro Ortega

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Abstract

This paper is focused on the solvability of a family of nonlinear elliptic systems defined in $\mathbb{R}^N$. Such equations contain Hardy potentials and Hardy-Sobolev criticalities coupled by a possible critical Hardy-Sobolev term. That problem arises as a generalization of Gross-Pitaevskii and Bose-Einstein type systems. By means of variational techniques, we shall find ground and bound states in terms of the coupling parameter $\nu$ and the order of the different parameters and exponents. In particular, for a wide range of parameters we find solutions as minimizers or Mountain-Pass critical points of the energy functional on the underlying Nehari manifold.

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Rafael López-Soriano, Alejandro Ortega. 2022-11-30. Nonlinear elliptic systems involving Hardy-Sobolev Criticalities. https://arxiv.org/abs/2211.17047

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