Degenerate elliptic problem with a singular nonlinearity

In this paper, we prove existence and regularity results for solutions of some nonlinear Dirichlet problems an elliptic equation defined by a degenerate coercive operator 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{ }\Omega u&=0 on \delta\Omega \end{array} \right. \end{equation} where $\Omega $ is bounded open subset $I\!\!R^{N}(N\geq2),$ $\gamma>0$ f$ nonnegative function that belongs to Lebesgue space.