2002-Fez conference on Partial Differental Equations,
Electron. J. Diff. Eqns., Conf. 09, 2002, pp. 139-147.

Nonlinear elliptic systems with exponential nonlinearities

Said El Manouni & Abdelfattah Touzani

Abstract:
In this paper we investigate the existence of solutions for
$$\displaylines{ -\mathop{\rm div}( a(| \nabla u | ^N)| \nabla u |^{N-2}u ) = f(x,u,v) \quad \hbox{in } \Omega \cr -\mathop{\rm div}(a(| \nabla v| ^N)| \nabla v |^{N-2}v )= g(x,u,v) \quad \hbox{in } \Omega \cr u(x) = v(x) = 0 \quad \hbox{on }\partial \Omega. }$$
Where $\Omega$ is a bounded domain in ${\mathbb{R}}^N$, $N\geq 2$, $f$ and $g$ are nonlinearities having an exponential growth on $\Omega$ and $a$ is a continuous function satisfying some conditions which ensure the existence of solutions.

Published December 28, 2002.
Subject classfications: 35J70, 35B45, 35B65.
Key words: Nonlinear elliptic system, exponential growth, Palais-Smale condition.

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Said El Manouni
Department of Mathematics and Informatic,
Faculty of Sciences Dhar-Mahraz,
P.O. Box 1796 Atlas-Fez, Morocco
e-mail: manouni@hotmail.com
Abdelfattah Touzani
Department of Mathematics and Informatic,
Faculty of Sciences Dhar-Mahraz,
P.O. Box 1796 Atlas-Fez, Morocco
e-mail: atouzani@iam.net.ma

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