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
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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
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Palabras clave: | Concentration compactness; Critical exponents; Sobolev embedding; Variable exponents |
Año: | 2017
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Volumen: | 24
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Número: | 2
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DOI: |
http://dx.doi.org/10.1007/s00030-017-0441-2 |
Título revista: | Nonlinear Differential Equations and Applications
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Título revista abreviado: | Nonlinear Diff. Equ. Appl.
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ISSN: | 10219722
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Registro: | https://bibliotecadigital.exactas.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