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Abstract:

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.

Registro:

Documento: Artículo
Título:Existence of solution to a critical equation with variable exponent
Autor:Bonder, J.F.; Saintier, N.; Silva, A.
Filiación:IMAS - CONICET, Universidad de Buenos Aires, Departamento de Matemática, FCEyN Ciudad Universitaria, Pabellón I (1428), Buenos Aires, Argentina
Universidad Nacional de General Sarmiento, Instituto de Ciencias, Juan María Gutierrez 1150 Los Polvorines, Pcia de Bs. As., Argentina
Universidad de Buenos Aires, Departamento de Matemática, FCEyN Ciudad Universitaria, Pabellón I (1428), Buenos Aires, Argentina
Palabras clave:Concentration compactness; Critical exponents; Sobolev embedding; Variable exponents
Año:2012
Volumen:37
Número:1
Página de inicio:579
Página de fin:594
DOI: http://dx.doi.org/10.5186/aasfm.2012.3743
Título revista:Annales Academiae Scientiarum Fennicae Mathematica
Título revista abreviado:Ann. Acad. Sci. Fenn. Math.
ISSN:1239629X
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_1239629X_v37_n1_p579_Bonder

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Citas:

---------- APA ----------
Bonder, J.F., Saintier, N. & Silva, A. (2012) . Existence of solution to a critical equation with variable exponent. Annales Academiae Scientiarum Fennicae Mathematica, 37(1), 579-594.
http://dx.doi.org/10.5186/aasfm.2012.3743
---------- CHICAGO ----------
Bonder, J.F., Saintier, N., Silva, A. "Existence of solution to a critical equation with variable exponent" . Annales Academiae Scientiarum Fennicae Mathematica 37, no. 1 (2012) : 579-594.
http://dx.doi.org/10.5186/aasfm.2012.3743
---------- MLA ----------
Bonder, J.F., Saintier, N., Silva, A. "Existence of solution to a critical equation with variable exponent" . Annales Academiae Scientiarum Fennicae Mathematica, vol. 37, no. 1, 2012, pp. 579-594.
http://dx.doi.org/10.5186/aasfm.2012.3743
---------- VANCOUVER ----------
Bonder, J.F., Saintier, N., Silva, A. Existence of solution to a critical equation with variable exponent. Ann. Acad. Sci. Fenn. Math. 2012;37(1):579-594.
http://dx.doi.org/10.5186/aasfm.2012.3743