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)
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__a167,
     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},
     year = {2014},
     volume = {2014},
     zbl = {1314.35042},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a167/}
}
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AU  - Saifia,  Ouarda
AU  - Vélin,  Jean
TI  - Existence and nonexistence of solutions to nonlinear gradient elliptic systems involving \((p(x),q(x))\)-Laplacian operators
JO  - Electronic journal of differential equations
PY  - 2014
VL  - 2014
UR  - http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a167/
LA  - en
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%0 Journal Article
%A Saifia,  Ouarda
%A Vélin,  Jean
%T Existence and nonexistence of solutions to nonlinear gradient elliptic systems involving \((p(x),q(x))\)-Laplacian operators
%J Electronic journal of differential equations
%D 2014
%V 2014
%U http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a167/
%G en
%F EJDE_2014__2014__a167
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__a167/