Abstract
The paper is focused on existence of nontrivial solutions of a Schrodinger-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.
Highlights
In this paper we prove existence of nontrivial solutions for the elliptic Schrodinger–Hardy system in the Heisenberg group Hn
The proof of Theorem 1.1 somehow follows [13], but there are some technical difficulties due to the more general setting considered in this paper, as well as to the presence of the Hardy terms and the critical nonlinearities
We briefly recall the relevant definitions and notations related to the Heisenberg group functional setting
Summary
Department of Mathematics and Informatics University of Perugia Via Vanvitelli, 1 06123 Perugia, Italy Dedicated to Professor Vicentiu D. Radulescu on the occasion of his 60th birthday, with high feelings of admiration for his notable contributions in Mathematics and great affection
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