In this paper, we prove existence and regularity results for solutions of some nonlinear Dirichlet problems for an elliptic equation defined by a degenerate coercive operator and a singular right hand side. \begin{ equation}\label{ 01} \left\{ \begin{ array}{ lll} -\displaystyle\mbox{ div}( a(x,u,\nabla u))&=\displaystyle\frac{ f}{ u^{ \gamma}} & \mbox{ in } \Omega \\ u&>0 &\mbox{ in }\Omega \\ u&=0 &\mbox{ on } \delta\Omega \end{ array} \right. \end{ equation} where $\Omega $ is bounded open subset of $I\!\!R^{ N}(N\geq2),$ $\gamma>0$ and $ f$ is a nonnegative function that belongs to some Lebesgue space.
Categories: math.AP