On positive solutions for classes of quasilinear singular problems

We study classes of quasilinear singular problems, involving the p -Laplacian operator and a potential, with homogeneous Dirichlet boundary condition. First, we prove the existence and regularity of positive solutions to a purely singular problem. Then, we investigate the existence of positive solutions with respect to a parameter depending on the behavior of the nonlinearities at infinity and at the origin. Finally, we extend some of these results to coupled system of equations. We use sub-super solution techniques to establish our results.