Existence of nontrivial weak solutions for a quasilinear Choquard equation

We are concerned with the following quasilinear Choquard equation: [Formula: see text] where [Formula: see text] , [Formula: see text] is the p-Laplacian operator, the potential function [Formula: see text] is continuous and [Formula: see text] . Here, [Formula: see text] is the Riesz potential of o...

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Detalles Bibliográficos
Autores principales: Lee, Jongrak, Kim, Jae-Myoung, Bae, Jung-Hyun, Park, Kisoeb
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2018
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5816830/
https://www.ncbi.nlm.nih.gov/pubmed/29497262
http://dx.doi.org/10.1186/s13660-018-1632-z
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author Lee, Jongrak
Kim, Jae-Myoung
Bae, Jung-Hyun
Park, Kisoeb
author_facet Lee, Jongrak
Kim, Jae-Myoung
Bae, Jung-Hyun
Park, Kisoeb
author_sort Lee, Jongrak
collection PubMed
description We are concerned with the following quasilinear Choquard equation: [Formula: see text] where [Formula: see text] , [Formula: see text] is the p-Laplacian operator, the potential function [Formula: see text] is continuous and [Formula: see text] . Here, [Formula: see text] is the Riesz potential of order [Formula: see text] . We study the existence of weak solutions for the problem above via the mountain pass theorem and the fountain theorem. Furthermore, we address the behavior of weak solutions to the problem near the origin under suitable assumptions for the nonlinear term f.
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spelling pubmed-58168302018-02-27 Existence of nontrivial weak solutions for a quasilinear Choquard equation Lee, Jongrak Kim, Jae-Myoung Bae, Jung-Hyun Park, Kisoeb J Inequal Appl Research We are concerned with the following quasilinear Choquard equation: [Formula: see text] where [Formula: see text] , [Formula: see text] is the p-Laplacian operator, the potential function [Formula: see text] is continuous and [Formula: see text] . Here, [Formula: see text] is the Riesz potential of order [Formula: see text] . We study the existence of weak solutions for the problem above via the mountain pass theorem and the fountain theorem. Furthermore, we address the behavior of weak solutions to the problem near the origin under suitable assumptions for the nonlinear term f. Springer International Publishing 2018-02-17 2018 /pmc/articles/PMC5816830/ /pubmed/29497262 http://dx.doi.org/10.1186/s13660-018-1632-z Text en © The Author(s) 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Lee, Jongrak
Kim, Jae-Myoung
Bae, Jung-Hyun
Park, Kisoeb
Existence of nontrivial weak solutions for a quasilinear Choquard equation
title Existence of nontrivial weak solutions for a quasilinear Choquard equation
title_full Existence of nontrivial weak solutions for a quasilinear Choquard equation
title_fullStr Existence of nontrivial weak solutions for a quasilinear Choquard equation
title_full_unstemmed Existence of nontrivial weak solutions for a quasilinear Choquard equation
title_short Existence of nontrivial weak solutions for a quasilinear Choquard equation
title_sort existence of nontrivial weak solutions for a quasilinear choquard equation
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5816830/
https://www.ncbi.nlm.nih.gov/pubmed/29497262
http://dx.doi.org/10.1186/s13660-018-1632-z
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AT baejunghyun existenceofnontrivialweaksolutionsforaquasilinearchoquardequation
AT parkkisoeb existenceofnontrivialweaksolutionsforaquasilinearchoquardequation

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