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On a class of nonlinear Schrödinger-Poisson systems involving a nonradial charge density / Carlo Mercuri; Teresa Megan Tyler

Revista Matemática Iberoamericana

Swansea University Author: Mercuri, Carlo

Abstract

In the spirit of the classical work of P. H. Rabinowitz on nonlinear Schrödinger equations, we prove existence of mountain-pass solutions and least energy solutions to a class of nonlinear Schrödinger-Poisson systems under different assumptions on a weight function at infinity. Our results cover a r...

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Published in: Revista Matemática Iberoamericana
Published:
Online Access: https://arxiv.org/abs/1805.00964
URI: https://cronfa.swan.ac.uk/Record/cronfa44664
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Abstract: In the spirit of the classical work of P. H. Rabinowitz on nonlinear Schrödinger equations, we prove existence of mountain-pass solutions and least energy solutions to a class of nonlinear Schrödinger-Poisson systems under different assumptions on a weight function at infinity. Our results cover a range of exponents, p,where the lack of compactness phenomena may be due to the combined effect of the invariance by translations of a `limiting problem' at infinity and of the possible unboundedness of the Palais-Smale sequences. Moreover, we find necessary conditions for concentration at points to occur for solutions to a singular perturbation of the same problem in various functional settings which are suitable for both variational and perturbation methods.
Keywords: Stationary Nonlinear Schrödinger-Poisson System, Weighted Sobolev Spaces, Palais-Smale Sequences, Lack of Compactness.
College: College of Science