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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Autores principales:	De Nápoli, P.L., Bonder, J.F., Silva, A.
Formato:	JOUR
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:	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	todo:paper_0362546X_v71_n12_p6283_DeNapoli
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spelling	todo:paper_0362546X_v71_n12_p6283_DeNapoli2023-10-03T15:27:22Z Multiple solutions for the p-Laplace operator with critical growth De Nápoli, P.L. Bonder, J.F. Silva, A. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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 Nápoli, P.L. Bonder, J.F. Silva, A. 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.
format	JOUR
author	De Nápoli, P.L. Bonder, J.F. Silva, A.
author_facet	De Nápoli, P.L. Bonder, J.F. Silva, A.
author_sort	De Nápoli, P.L.
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
url	http://hdl.handle.net/20.500.12110/paper_0362546X_v71_n12_p6283_DeNapoli
work_keys_str_mv	AT denapolipl multiplesolutionsfortheplaplaceoperatorwithcriticalgrowth AT bonderjf multiplesolutionsfortheplaplaceoperatorwithcriticalgrowth AT silvaa multiplesolutionsfortheplaplaceoperatorwithcriticalgrowth
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Multiple solutions for the p-Laplace operator with critical growth

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