Existence and boundedness of solutions for a singular cooperative quasilinear elliptic system

This article sets forth results on the existence, a priori estimates and boundedness of positive solutions of a singular quasilinear system of elliptic equations. The systems studied here have in the principal part different p-Laplacians with Dirichlet boundary condition on a bounded domain. The approach is based on the sub-supersolution methods for systems of quasilinear equations combined with perturbation arguments involving singular terms. The structure of the singular terms in the system is essentially used to construct the sub-supersolution. A Moser iteration procedure is also obtained for our class of singular systems establishing a priori estimates and boundedness of solutions.