Geodesic
Existence and nonexistence of solutions to nonlinear gradient elliptic systems involving $(p(x),q(x))$-Laplacian operators
Electronic Journal of Differential Equations, Tome 2014 (2014).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 35J20, 35J35, 35J45, 35J50, 35J60, 35J70
Keywords: fibering method, $p(x)$-Laplacian, generalized pohozeav identity, pucci-serrin identity 
@article{EJDE_2014__2014__a67,
     author = {Saifia, Ouarda and V\'elin, Jean},
     title = {Existence and nonexistence of solutions to nonlinear gradient elliptic systems involving $(p(x),q(x))${-Laplacian} operators},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2014},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a67/}
}
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Saifia, Ouarda; Vélin, Jean. Existence and nonexistence of solutions to nonlinear gradient elliptic systems involving $(p(x),q(x))$-Laplacian operators. Electronic Journal of Differential Equations, Tome 2014 (2014). http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a67/