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Abstract:

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.

Registro:

Documento: Artículo
Título:Multiple solutions for the p(x) - Laplace operator with critical growth
Autor:Silva, A.
Filiación:Department of Mathematics, University of Buenos Aires, (1428) Buenos Aires, Argentina
Palabras clave:Concentration-compactness principle; Variable exponent spaces
Año:2011
Volumen:11
Número:1
Página de inicio:63
Página de fin:75
DOI: http://dx.doi.org/10.1515/ans-2011-0103
Título revista:Advanced Nonlinear Studies
Título revista abreviado:Adv. Nonlinear Stud.
ISSN:15361365
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15361365_v11_n1_p63_Silva

Referencias:

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Citas:

---------- APA ----------
(2011) . Multiple solutions for the p(x) - Laplace operator with critical growth. Advanced Nonlinear Studies, 11(1), 63-75.
http://dx.doi.org/10.1515/ans-2011-0103
---------- CHICAGO ----------
Silva, A. "Multiple solutions for the p(x) - Laplace operator with critical growth" . Advanced Nonlinear Studies 11, no. 1 (2011) : 63-75.
http://dx.doi.org/10.1515/ans-2011-0103
---------- MLA ----------
Silva, A. "Multiple solutions for the p(x) - Laplace operator with critical growth" . Advanced Nonlinear Studies, vol. 11, no. 1, 2011, pp. 63-75.
http://dx.doi.org/10.1515/ans-2011-0103
---------- VANCOUVER ----------
Silva, A. Multiple solutions for the p(x) - Laplace operator with critical growth. Adv. Nonlinear Stud. 2011;11(1):63-75.
http://dx.doi.org/10.1515/ans-2011-0103