Existence of solutions for an elliptic problem with degenerate coercivity.

  • Aharrouch Benali university sidi mohamed ben abdellah faculty of sciences fes
  • Bennouna. Jaouad Sidi Mohamed Ben Abdellah University,\\ Faculty of Sciences Dhar El Mahraz Laboratory LAMA, Department of Mathematics P.O. Box 1796 Atlas Fez, Morocco


We study the existence of solutions for the following problem $$\left\{\begin{array}{lll} A(u)+H(x,u,\nabla u)=f &\mbox{in}& \Omega,\\ u=0 &\mbox{on} &\partial\Omega, \end{array}\right.$$ where, $A$ is a Loray-Lions operator from $W_0^{1,p}(\Omega, \nu)$ into its dual, while $H(x,s,\xi)$ is a nonlinear term witch has a growth condition with respect to $\xi$. For the right hand side $f$, we will make a different assumptions.