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On a class of nonlinear Schrödinger–Poisson systems involving a nonradial charge density

Carlo Mercuri, Megan Tyler

Revista Matemática Iberoamericana

Swansea 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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first_indexed 2018-10-01T18:59:55Z
last_indexed 2023-01-11T14:21:21Z
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spelling 2022-12-05T15:57:28.1466551 v2 44664 2018-10-01 On a class of nonlinear Schrödinger–Poisson systems involving a nonradial charge density 46bf09624160610d6d6cf435996a5913 Carlo Mercuri Carlo Mercuri true false 4b929e04790494ce58094f4ccc2f7f3e Megan Tyler Megan Tyler true false 2018-10-01 FGSEN 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. Journal Article Revista Matemática Iberoamericana European Mathematical Society Publishing House 0213-2230 Stationary Nonlinear Schrödinger-Poisson System, Weighted Sobolev Spaces, Palais-Smale Sequences, Lack of Compactness. 7 1 2020 2020-01-07 10.4171/rmi/1158 COLLEGE NANME Science and Engineering - Faculty COLLEGE CODE FGSEN Swansea University 2022-12-05T15:57:28.1466551 2018-10-01T18:03:20.4195777 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Carlo Mercuri 1 Megan Tyler 2 44664__11331__2cc74a76246a4f0491651b969f7861c7.pdf MercuriTyleracceptedversion.pdf 2018-10-01T18:06:27.3900000 Output 537646 application/pdf Accepted Manuscript true 2018-10-01T00:00:00.0000000 true eng
title On a class of nonlinear Schrödinger–Poisson systems involving a nonradial charge density
spellingShingle On a class of nonlinear Schrödinger–Poisson systems involving a nonradial charge density
Carlo Mercuri
Megan Tyler
title_short On a class of nonlinear Schrödinger–Poisson systems involving a nonradial charge density
title_full On a class of nonlinear Schrödinger–Poisson systems involving a nonradial charge density
title_fullStr On a class of nonlinear Schrödinger–Poisson systems involving a nonradial charge density
title_full_unstemmed On a class of nonlinear Schrödinger–Poisson systems involving a nonradial charge density
title_sort On a class of nonlinear Schrödinger–Poisson systems involving a nonradial charge density
author_id_str_mv 46bf09624160610d6d6cf435996a5913
4b929e04790494ce58094f4ccc2f7f3e
author_id_fullname_str_mv 46bf09624160610d6d6cf435996a5913_***_Carlo Mercuri
4b929e04790494ce58094f4ccc2f7f3e_***_Megan Tyler
author Carlo Mercuri
Megan Tyler
author2 Carlo Mercuri
Megan Tyler
format Journal article
container_title Revista Matemática Iberoamericana
publishDate 2020
institution Swansea University
issn 0213-2230
doi_str_mv 10.4171/rmi/1158
publisher European Mathematical Society Publishing House
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
document_store_str 1
active_str 0
description 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.
published_date 2020-01-07T03:55:59Z
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score 11.037056

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