Multiple solutions for the p-Laplace operator with critical growth

In this paper we show the existence of at least three nontrivial solutions to the following quasilinear elliptic equation - Δp u = | u |p* - 2 u + λ f (x, u) in a smooth bounded domain Ω of RN with homogeneous Dirichlet boundary conditions on ∂ Ω, where p* = N p / (N - p) is the critical Sobolev exp...

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Detalles Bibliográficos
Autores principales:	De Napoli, Pablo Luis, Silva, Analia Concepcion
Publicado:	2009
Materias:	Critical growth p-Laplace equations Variational methods Bounded domain Critical Sobolev exponent Dirichlet boundary condition Multiple solutions Nontrivial solution P-Laplace equations P-Laplace operator P-Laplacian Quasilinear elliptic equations Laplace transforms Mathematical operators Nonlinear equations Laplace equation
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0362546X_v71_n12_p6283_DeNapoli http://hdl.handle.net/20.500.12110/paper_0362546X_v71_n12_p6283_DeNapoli
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_0362546X_v71_n12_p6283_DeNapoli
record_format	dspace
spelling	paper:paper_0362546X_v71_n12_p6283_DeNapoli2023-06-08T15:35:23Z Multiple solutions for the p-Laplace operator with critical growth De Napoli, Pablo Luis Silva, Analia Concepcion Critical growth p-Laplace equations Variational methods Bounded domain Critical growth Critical Sobolev exponent Dirichlet boundary condition Multiple solutions Nontrivial solution P-Laplace equations P-Laplace operator P-Laplacian Quasilinear elliptic equations Variational methods Laplace transforms Mathematical operators Nonlinear equations Laplace equation In this paper we show the existence of at least three nontrivial solutions to the following quasilinear elliptic equation - Δp u = \| u \|p* - 2 u + λ f (x, u) in a smooth bounded domain Ω of RN with homogeneous Dirichlet boundary conditions on ∂ Ω, where p* = N p / (N - p) is the critical Sobolev exponent and Δp u = div (\| ∇ u \|p - 2 ∇ u) is the p-Laplacian. The proof is based on variational arguments and the classical concentration compactness method. © 2009 Elsevier Ltd. All rights reserved. Fil:De Nápoli, P.L. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Silva, A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2009 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0362546X_v71_n12_p6283_DeNapoli http://hdl.handle.net/20.500.12110/paper_0362546X_v71_n12_p6283_DeNapoli
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Critical growth p-Laplace equations Variational methods Bounded domain Critical growth Critical Sobolev exponent Dirichlet boundary condition Multiple solutions Nontrivial solution P-Laplace equations P-Laplace operator P-Laplacian Quasilinear elliptic equations Variational methods Laplace transforms Mathematical operators Nonlinear equations Laplace equation
spellingShingle	Critical growth p-Laplace equations Variational methods Bounded domain Critical growth Critical Sobolev exponent Dirichlet boundary condition Multiple solutions Nontrivial solution P-Laplace equations P-Laplace operator P-Laplacian Quasilinear elliptic equations Variational methods Laplace transforms Mathematical operators Nonlinear equations Laplace equation De Napoli, Pablo Luis Silva, Analia Concepcion Multiple solutions for the p-Laplace operator with critical growth
topic_facet	Critical growth p-Laplace equations Variational methods Bounded domain Critical growth Critical Sobolev exponent Dirichlet boundary condition Multiple solutions Nontrivial solution P-Laplace equations P-Laplace operator P-Laplacian Quasilinear elliptic equations Variational methods Laplace transforms Mathematical operators Nonlinear equations Laplace equation
description	In this paper we show the existence of at least three nontrivial solutions to the following quasilinear elliptic equation - Δp u = \| u \|p* - 2 u + λ f (x, u) in a smooth bounded domain Ω of RN with homogeneous Dirichlet boundary conditions on ∂ Ω, where p* = N p / (N - p) is the critical Sobolev exponent and Δp u = div (\| ∇ u \|p - 2 ∇ u) is the p-Laplacian. The proof is based on variational arguments and the classical concentration compactness method. © 2009 Elsevier Ltd. All rights reserved.
author	De Napoli, Pablo Luis Silva, Analia Concepcion
author_facet	De Napoli, Pablo Luis Silva, Analia Concepcion
author_sort	De Napoli, Pablo Luis
title	Multiple solutions for the p-Laplace operator with critical growth
title_short	Multiple solutions for the p-Laplace operator with critical growth
title_full	Multiple solutions for the p-Laplace operator with critical growth
title_fullStr	Multiple solutions for the p-Laplace operator with critical growth
title_full_unstemmed	Multiple solutions for the p-Laplace operator with critical growth
title_sort	multiple solutions for the p-laplace operator with critical growth
publishDate	2009
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0362546X_v71_n12_p6283_DeNapoli http://hdl.handle.net/20.500.12110/paper_0362546X_v71_n12_p6283_DeNapoli
work_keys_str_mv	AT denapolipabloluis multiplesolutionsfortheplaplaceoperatorwithcriticalgrowth AT silvaanaliaconcepcion multiplesolutionsfortheplaplaceoperatorwithcriticalgrowth
_version_	1768545190567477248

Multiple solutions for the p-Laplace operator with critical growth

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