Multiple solutions for the p(x) - Laplace operator with critical growth

The aim of this paper is to extend previous results regarding the multiplicity of solutions for quasilinear elliptic problems with critical growth to the variable exponent case. We prove, in the spirit of [4], the existence of at least three nontrivial solutions to the quasilinear elliptic equation...

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Autor principal: Silva, A.
Formato: JOUR
Materias:
Concentration-compactness principle
Variable exponent spaces
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_15361365_v11_n1_p63_Silva
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_15361365_v11_n1_p63_Silva2023-10-03T16:21:47Z Multiple solutions for the p(x) - Laplace operator with critical growth Silva, A. Concentration-compactness principle Variable exponent spaces The aim of this paper is to extend previous results regarding the multiplicity of solutions for quasilinear elliptic problems with critical growth to the variable exponent case. We prove, in the spirit of [4], the existence of at least three nontrivial solutions to the quasilinear elliptic equation -Δp(x)u = |u|q(x)-2u + λf (x, u) in a smooth bounded domain Ω of RN with homogeneous Dirichlet boundary conditions on ∂Ω. We assume that {q(x) = p*(x)} ≠ θ, where p*(x) = Np(x)/(N - p(x)) is the critical Sobolev exponent for variable exponents and Δp(x)u = div(|∇u| p(x)-2∇u) is the p(x)-laplacian. The proof is based on variational arguments and the extension of concentration compactness method for variable exponent spaces. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_15361365_v11_n1_p63_Silva
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Concentration-compactness principle
Variable exponent spaces
spellingShingle Concentration-compactness principle
Variable exponent spaces
Silva, A.
Multiple solutions for the p(x) - Laplace operator with critical growth
topic_facet Concentration-compactness principle
Variable exponent spaces
description The aim of this paper is to extend previous results regarding the multiplicity of solutions for quasilinear elliptic problems with critical growth to the variable exponent case. We prove, in the spirit of [4], the existence of at least three nontrivial solutions to the quasilinear elliptic equation -Δp(x)u = |u|q(x)-2u + λf (x, u) in a smooth bounded domain Ω of RN with homogeneous Dirichlet boundary conditions on ∂Ω. We assume that {q(x) = p*(x)} ≠ θ, where p*(x) = Np(x)/(N - p(x)) is the critical Sobolev exponent for variable exponents and Δp(x)u = div(|∇u| p(x)-2∇u) is the p(x)-laplacian. The proof is based on variational arguments and the extension of concentration compactness method for variable exponent spaces.
format JOUR
author Silva, A.
author_facet Silva, A.
author_sort Silva, A.
title Multiple solutions for the p(x) - Laplace operator with critical growth
title_short Multiple solutions for the p(x) - Laplace operator with critical growth
title_full Multiple solutions for the p(x) - Laplace operator with critical growth
title_fullStr Multiple solutions for the p(x) - Laplace operator with critical growth
title_full_unstemmed Multiple solutions for the p(x) - Laplace operator with critical growth
title_sort multiple solutions for the p(x) - laplace operator with critical growth
url http://hdl.handle.net/20.500.12110/paper_15361365_v11_n1_p63_Silva
work_keys_str_mv AT silvaa multiplesolutionsforthepxlaplaceoperatorwithcriticalgrowth
_version_ 1782028300213813248

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