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Groundstates and infinitely many high energy solutions to a class of nonlinear Schrödinger–Poisson systems

Tomas Dutko, Carlo Mercuri Orcid Logo, Megan Tyler

Calculus of Variations and Partial Differential Equations, Volume: 60, Issue: 5

Swansea University Authors: Carlo Mercuri Orcid Logo, Megan Tyler

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DOI (Published version): 10.1007/s00526-021-02045-y

Abstract

We study a nonlinear Schrödinger-Poisson system which reduces to a nonlinear andnonlocal PDE set on the whole spatial domain, whose variational formulation requires propertiesof a suitable finite energy space, such as separability and compactness, that we study and use.Our equation involves a weight...

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Published in: Calculus of Variations and Partial Differential Equations
ISSN: 0944-2669 1432-0835
Published: Springer Science and Business Media LLC 2021
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URI: https://cronfa.swan.ac.uk/Record/cronfa57454
first_indexed 2021-07-27T08:28:36Z
last_indexed 2025-02-26T05:24:46Z
id cronfa57454
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spelling 2025-02-25T14:10:26.6518634 v2 57454 2021-07-27 Groundstates and infinitely many high energy solutions to a class of nonlinear Schrödinger–Poisson systems 46bf09624160610d6d6cf435996a5913 0000-0002-4289-5573 Carlo Mercuri Carlo Mercuri true false 4b929e04790494ce58094f4ccc2f7f3e Megan Tyler Megan Tyler true false 2021-07-27 MACS We study a nonlinear Schrödinger-Poisson system which reduces to a nonlinear andnonlocal PDE set on the whole spatial domain, whose variational formulation requires propertiesof a suitable finite energy space, such as separability and compactness, that we study and use.Our equation involves a weight function which is allowed as particular scenarios, to either 1) vanish on a region and be finite at infinity, or 2) be large at infinity. We find least energy solutionsin both cases, studying the vanishing case by means of a priori integral bounds on sequences ofapproximating solutions and highlighting the role of certain positive universal constants for thesebounds to hold. Within the Ljusternik-Schnirelman theory we show the existence of infinitelymany distinct pairs of high energy solutions, having a min-max characterisation given by meansof the Krasnoselskii genus. Journal Article Calculus of Variations and Partial Differential Equations 60 5 Springer Science and Business Media LLC 0944-2669 1432-0835 Nonlinear Schrödinger–Poisson system; Weighted Sobolev spaces; Palais–Smale sequences; Compactness; Multiple solutions; Nonexistence 27 7 2021 2021-07-27 10.1007/s00526-021-02045-y COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University 2025-02-25T14:10:26.6518634 2021-07-27T09:23:50.7638712 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Tomas Dutko 1 Carlo Mercuri 0000-0002-4289-5573 2 Megan Tyler 3 57454__20483__e9890b16e92d4ebb82c4c2da4d926470.pdf 57454.pdf 2021-07-28T17:29:39.9229784 Output 559421 application/pdf Accepted Manuscript true 2022-07-27T00:00:00.0000000 true eng
title Groundstates and infinitely many high energy solutions to a class of nonlinear Schrödinger–Poisson systems
spellingShingle Groundstates and infinitely many high energy solutions to a class of nonlinear Schrödinger–Poisson systems
Carlo Mercuri
Megan Tyler
title_short Groundstates and infinitely many high energy solutions to a class of nonlinear Schrödinger–Poisson systems
title_full Groundstates and infinitely many high energy solutions to a class of nonlinear Schrödinger–Poisson systems
title_fullStr Groundstates and infinitely many high energy solutions to a class of nonlinear Schrödinger–Poisson systems
title_full_unstemmed Groundstates and infinitely many high energy solutions to a class of nonlinear Schrödinger–Poisson systems
title_sort Groundstates and infinitely many high energy solutions to a class of nonlinear Schrödinger–Poisson systems
author_id_str_mv 46bf09624160610d6d6cf435996a5913
4b929e04790494ce58094f4ccc2f7f3e
author_id_fullname_str_mv 46bf09624160610d6d6cf435996a5913_***_Carlo Mercuri
4b929e04790494ce58094f4ccc2f7f3e_***_Megan Tyler
author Carlo Mercuri
Megan Tyler
author2 Tomas Dutko
Carlo Mercuri
Megan Tyler
format Journal article
container_title Calculus of Variations and Partial Differential Equations
container_volume 60
container_issue 5
publishDate 2021
institution Swansea University
issn 0944-2669
1432-0835
doi_str_mv 10.1007/s00526-021-02045-y
publisher Springer Science and Business Media LLC
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 We study a nonlinear Schrödinger-Poisson system which reduces to a nonlinear andnonlocal PDE set on the whole spatial domain, whose variational formulation requires propertiesof a suitable finite energy space, such as separability and compactness, that we study and use.Our equation involves a weight function which is allowed as particular scenarios, to either 1) vanish on a region and be finite at infinity, or 2) be large at infinity. We find least energy solutionsin both cases, studying the vanishing case by means of a priori integral bounds on sequences ofapproximating solutions and highlighting the role of certain positive universal constants for thesebounds to hold. Within the Ljusternik-Schnirelman theory we show the existence of infinitelymany distinct pairs of high energy solutions, having a min-max characterisation given by meansof the Krasnoselskii genus.
published_date 2021-07-27T04:56:38Z
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score 11.089386

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