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Abstract:

The purpose of this paper is to formulate sufficient existence conditions for a critical equation involving the p(x)-Laplacian of the form (0.1) below posed in RN. This equation is critical in the sense that the source term has the form K(x) | u| q ( x ) - 2u with an exponent q that can be equal to the critical exponent p∗ at some points of RN including at infinity. The sufficient existence condition we find are local in the sense that they depend only on the behaviour of the exponents p and q near these points. We stress that we do not assume any symmetry or periodicity of the coefficients of the equation and that K is not required to vanish in some sense at infinity like in most existing results. The proof of these local existence conditions is based on a notion of localized best Sobolev constant at infinity and a refined concentration-compactness at infinity. © 2017, Springer International Publishing.

Registro:

Documento: Artículo
Título:Local existence conditions for an equations involving the p(x) -Laplacian with critical exponent in RN
Autor:Saintier, N.; Silva, A.
Filiación:Departamento de Matemática, FCEyN - Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I (1428), Buenos Aires, Argentina
Instituto de Matemática Aplicada San Luis, IMASL, Universidad Nacional de San Luis and CONICET, Ejercito de los Andes 950, San Luis, D5700HHW, Argentina
Palabras clave:Concentration compactness; Critical exponents; Sobolev embedding; Variable exponents
Año:2017
Volumen:24
Número:2
DOI: http://dx.doi.org/10.1007/s00030-017-0441-2
Título revista:Nonlinear Differential Equations and Applications
Título revista abreviado:Nonlinear Diff. Equ. Appl.
ISSN:10219722
Registro:http://digital.bl.fcen.uba.ar/collection/paper/document/paper_10219722_v24_n2_p_Saintier

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Citas:

---------- APA ----------
Saintier, N. & Silva, A. (2017) . Local existence conditions for an equations involving the p(x) -Laplacian with critical exponent in RN. Nonlinear Differential Equations and Applications, 24(2).
http://dx.doi.org/10.1007/s00030-017-0441-2
---------- CHICAGO ----------
Saintier, N., Silva, A. "Local existence conditions for an equations involving the p(x) -Laplacian with critical exponent in RN" . Nonlinear Differential Equations and Applications 24, no. 2 (2017).
http://dx.doi.org/10.1007/s00030-017-0441-2
---------- MLA ----------
Saintier, N., Silva, A. "Local existence conditions for an equations involving the p(x) -Laplacian with critical exponent in RN" . Nonlinear Differential Equations and Applications, vol. 24, no. 2, 2017.
http://dx.doi.org/10.1007/s00030-017-0441-2
---------- VANCOUVER ----------
Saintier, N., Silva, A. Local existence conditions for an equations involving the p(x) -Laplacian with critical exponent in RN. Nonlinear Diff. Equ. Appl. 2017;24(2).
http://dx.doi.org/10.1007/s00030-017-0441-2