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

Revista Matemática Iberoamericana

Swansesa University Authors: Carlo, Mercuri, Megan, Tyler

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DOI (Published version): 10.4171/rmi/1158

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
ISSN: 0213-2230
Published: European Mathematical Society Publishing House 2020
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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.