Necessary and sufficient conditions for the existence of nonnegative solutions of inhomogeneous p-Laplace equation*

Let ω be a smooth bounded domain in Rn. In this article, we consider the homogeneous boundary Dirichlet problem of inhomogeneous p-Laplace equation -Δpu = |u|q-1u+λf(x) on ω, and identify necessary and sufficient conditions on ω and f(x) which ensure the existence, or multiplicities of nonnegative solutions for the problem under consideration.