Electronic Journal of Differential Equations,
Conference 09 (2002), pp. 139-147.

Title: Nonlinear elliptic systems with exponential nonlinearities.

Authors: Said El Manouni (Faculte des Sciences Dhar-Mahraz, Fes, Maroc)
  Abdelfattah Touzani (Faculte des Sciences Dhar-Mahraz, Fes, Maroc)
 
Abstract: 
  In this paper we investigate the existence of solutions for
  \begin{gather*}
  -\mathop{\rm div}( a(| \nabla u | ^N)| \nabla u |^{N-2}u ) =
  f(x,u,v) \quad \mbox{in } \Omega \\
  -\mathop{\rm div}(a(| \nabla v| ^N)| \nabla v |^{N-2}v )= g(x,u,v)
  \quad \mbox{in } \Omega \\
  u(x) = v(x) = 0   \quad \mbox{on }\partial \Omega.
  \end{gather*}
  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.
Math Subject Classifications: 35J70, 35B45, 35B65.
Key Words: Nonlinear elliptic system; exponential growth; Palais-Smale condition.