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

Consider the Dirichlet problem for an inhomogeneous $p$-Laplace equation with nonlinear source in presence of external mass forces, we obtain new sufficient conditions for the existence of a weak nonnegative bounded solution. The conditions are written in explicit form in terms of the data of the problem.