On the existence of nonnegative solutions to the Dirichlet boundary value problem for the p-Laplace equation in the presence of exterior mass forces

Abstract

We consider the Dirichlet problem for an inhomogeneous p-Laplace equation with nonlinear source in the presence of exterior mass forces.We obtain new sufficient conditions for the existence of a weak nonnegative bounded solution. The sufficient conditions are written in explicit form through the data of the problem.