Critical Schrödinger-Hardy systems in the Heisenberg group

Patrizia Pucci

doi:10.3934/dcdss.2019025

Article Contents

2019, Volume 12, Issue 2: 375-400. Doi: 10.3934/dcdss.2019025

This issue Previous Article Multiple solutions for (p, 2)-equations at resonance Next Article Infinitely many symmetric solutions for anisotropic problems driven by nonhomogeneous operators

Critical Schrödinger-Hardy systems in the Heisenberg group

Patrizia Pucci

Department of Mathematics and Informatics, University of Perugia, Via Vanvitelli, 1, 06123 Perugia, Italy

Received: May 2017

Revised: December 2017

Published: April 2019

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Abstract

The paper is focused on existence of nontrivial solutions of a Schrödinger-Hardy system in the Heisenberg group, involving critical nonlinearities. Existence is obtained by an application of the mountain pass theorem and the Ekeland variational principle, but there are several difficulties arising in the framework of Heisenberg groups, also due to the presence of the Hardy terms as well as critical nonlinearities.

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Mathematics Subject Classification: Primary: 35R03, 35H20, 35J70; Secondary: 35B33, 35A15.

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