Nonlinear Singular Elliptic Equations of p-Laplace Type with Superlinear Growth in the Gradient

We consider a singular nonlinear elliptic Dirichlet problems with lower-order terms, where the combined effects of a superlinear growth in the gradient and a singular term allow us to establish some existence and regularity results. The model problem is {- div(|del u|p-2 del u) + mu|u|p-1u = b(x) |del u|(q) u theta+ f(x) u gamma in Omega,u = 0 on partial derivative Omega, (0.1) where Omega is an open and bounded subset of RN , mu >= 0, 0 < theta < 1, 0 < theta < 1 and f is a nonnegative function that belong to some Lebesgue space.