Infinitely Many Weak Solutions of the p-Laplacian Equation with Nonlinear Boundary Conditions

We study the following p-Laplacian equation with nonlinear boundary conditions: −Δ(p) u + μ(x) | u|(p−2) u = f(x, u) + g(x, u), x ∈ Ω, | ∇u|(p−2)∂u/∂n = η | u|(p−2) u and x ∈ ∂Ω, where Ω is a bounded domain in ℝ(N) with smooth boundary ∂Ω. We prove that the equation has infinitely many weak solution...

Descripción completa

Detalles Bibliográficos
Autores principales: Lu, Feng-Yun, Deng, Gui-Qian
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2014
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3914418/
https://www.ncbi.nlm.nih.gov/pubmed/24574872
http://dx.doi.org/10.1155/2014/194310
_version_ 1782302403210510336
author Lu, Feng-Yun
Deng, Gui-Qian
author_facet Lu, Feng-Yun
Deng, Gui-Qian
author_sort Lu, Feng-Yun
collection PubMed
description We study the following p-Laplacian equation with nonlinear boundary conditions: −Δ(p) u + μ(x) | u|(p−2) u = f(x, u) + g(x, u), x ∈ Ω, | ∇u|(p−2)∂u/∂n = η | u|(p−2) u and x ∈ ∂Ω, where Ω is a bounded domain in ℝ(N) with smooth boundary ∂Ω. We prove that the equation has infinitely many weak solutions by using the variant fountain theorem due to Zou (2001) and f, g do not need to satisfy the (P.S) or (P.S*) condition.
format Online
Article
Text
id pubmed-3914418
institution National Center for Biotechnology Information
language English
publishDate 2014
publisher Hindawi Publishing Corporation
record_format MEDLINE/PubMed
spelling pubmed-39144182014-02-26 Infinitely Many Weak Solutions of the p-Laplacian Equation with Nonlinear Boundary Conditions Lu, Feng-Yun Deng, Gui-Qian ScientificWorldJournal Research Article We study the following p-Laplacian equation with nonlinear boundary conditions: −Δ(p) u + μ(x) | u|(p−2) u = f(x, u) + g(x, u), x ∈ Ω, | ∇u|(p−2)∂u/∂n = η | u|(p−2) u and x ∈ ∂Ω, where Ω is a bounded domain in ℝ(N) with smooth boundary ∂Ω. We prove that the equation has infinitely many weak solutions by using the variant fountain theorem due to Zou (2001) and f, g do not need to satisfy the (P.S) or (P.S*) condition. Hindawi Publishing Corporation 2014-01-14 /pmc/articles/PMC3914418/ /pubmed/24574872 http://dx.doi.org/10.1155/2014/194310 Text en Copyright © 2014 F.-Y. Lu and G.-Q. Deng. https://creativecommons.org/licenses/by/3.0/ This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Article
Lu, Feng-Yun
Deng, Gui-Qian
Infinitely Many Weak Solutions of the p-Laplacian Equation with Nonlinear Boundary Conditions
title Infinitely Many Weak Solutions of the p-Laplacian Equation with Nonlinear Boundary Conditions
title_full Infinitely Many Weak Solutions of the p-Laplacian Equation with Nonlinear Boundary Conditions
title_fullStr Infinitely Many Weak Solutions of the p-Laplacian Equation with Nonlinear Boundary Conditions
title_full_unstemmed Infinitely Many Weak Solutions of the p-Laplacian Equation with Nonlinear Boundary Conditions
title_short Infinitely Many Weak Solutions of the p-Laplacian Equation with Nonlinear Boundary Conditions
title_sort infinitely many weak solutions of the p-laplacian equation with nonlinear boundary conditions
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3914418/
https://www.ncbi.nlm.nih.gov/pubmed/24574872
http://dx.doi.org/10.1155/2014/194310
work_keys_str_mv AT lufengyun infinitelymanyweaksolutionsoftheplaplacianequationwithnonlinearboundaryconditions
AT dengguiqian infinitelymanyweaksolutionsoftheplaplacianequationwithnonlinearboundaryconditions

Ejemplares similares