Existence of positive radial solutions for a superlinear semipositone p-Laplacian problem on the exterior of a ball

Abstract

We prove the existence of positive radial solutions to a class of semipositone p-Laplacian problems on the exterior of a ball subject to Dirichlet and nonlinear boundary conditions. Using variational methods we prove the existence of a solution, and then use a priori estimates to prove the positivity of the solution.