Existence of solution to a critical equation with variable exponent

In this paper we study the existence problem for the p(x)-Laplacian operator with a nonlinear critical source. We find a local condition on the exponents ensuring the existence of a nontrivial solution that shows that the Pohozaev obstruction does not holds in general in the variable exponent settin...

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Detalles Bibliográficos
Autores principales: Bonder, J.F., Saintier, N., Silva, A.
Formato: JOUR
Materias:
Concentration compactness
Critical exponents
Sobolev embedding
Variable exponents
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_1239629X_v37_n1_p579_Bonder
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_1239629X_v37_n1_p579_Bonder2023-10-03T16:09:11Z Existence of solution to a critical equation with variable exponent Bonder, J.F. Saintier, N. Silva, A. Concentration compactness Critical exponents Sobolev embedding Variable exponents In this paper we study the existence problem for the p(x)-Laplacian operator with a nonlinear critical source. We find a local condition on the exponents ensuring the existence of a nontrivial solution that shows that the Pohozaev obstruction does not holds in general in the variable exponent setting. The proof relies on the Concentration-Compactness Principle for variable exponents and the Mountain Pass Theorem. 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_1239629X_v37_n1_p579_Bonder
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
Critical exponents
Sobolev embedding
Variable exponents
spellingShingle Concentration compactness
Critical exponents
Sobolev embedding
Variable exponents
Bonder, J.F.
Saintier, N.
Silva, A.
Existence of solution to a critical equation with variable exponent
topic_facet Concentration compactness
Critical exponents
Sobolev embedding
Variable exponents
description In this paper we study the existence problem for the p(x)-Laplacian operator with a nonlinear critical source. We find a local condition on the exponents ensuring the existence of a nontrivial solution that shows that the Pohozaev obstruction does not holds in general in the variable exponent setting. The proof relies on the Concentration-Compactness Principle for variable exponents and the Mountain Pass Theorem.
format JOUR
author Bonder, J.F.
Saintier, N.
Silva, A.
author_facet Bonder, J.F.
Saintier, N.
Silva, A.
author_sort Bonder, J.F.
title Existence of solution to a critical equation with variable exponent
title_short Existence of solution to a critical equation with variable exponent
title_full Existence of solution to a critical equation with variable exponent
title_fullStr Existence of solution to a critical equation with variable exponent
title_full_unstemmed Existence of solution to a critical equation with variable exponent
title_sort existence of solution to a critical equation with variable exponent
url http://hdl.handle.net/20.500.12110/paper_1239629X_v37_n1_p579_Bonder
work_keys_str_mv AT bonderjf existenceofsolutiontoacriticalequationwithvariableexponent
AT saintiern existenceofsolutiontoacriticalequationwithvariableexponent
AT silvaa existenceofsolutiontoacriticalequationwithvariableexponent
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