Electron. J. Diff. Equ., Vol. 2014 (2014), No. 163, pp. 1-22.

Existence and nonexistence of solutions to nonlinear gradient elliptic systems involving (p(x),q(x))-Laplacian operators

Ouarda Saifia, Jean Velin

In this article, we establish the existence of nontrivial solutions by employing the fibering method introduced by Pohozaev. We also generalize the well-known Pohozaev and Pucci-Serrin identities to a (p(x),q(x))-Laplacian system. A nonexistence result for a such system is then proved.

Submitted April 2, 2014. Published July 25, 2014.
Math Subject Classifications: 35J20, 35J35, 35J45, 35J50, 35J60, 35J70.
Key Words: Fibering method; p(x)-Laplacian; Generalized Pohozeav identity; Pucci-Serrin identity.

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Ouarda Saifia
Department of mathematics, University of Annaba
PO 12, El Hadjar, 23000, Annaba, Algeria
email: wsaifia@gmail.com
Jean Vélin
Department of Mathematics and Computers, Laboratory CEREGMIA
University of Antilles-Guyane, Campus de Fouillole
97159 Pointe-&aagrave;-Pitre, Guadeloupe (French West Indies)
email: jean.velin@univ-ag.fr

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