Antimaximum principle in exterior domains

We consider the antimaximum principle for the p-Laplacian in the exterior domain: {-Δpu=λK(x)|u|p-2u+h(x)in B1c,u=0on ∂B1, where Δp is the p-Laplace operator with p>1,λ is the spectral parameter and B1c is the exterior of the closed unit ball in RN with N ≥ 1. The function h is assumed to be nonnegative and nonzero, however the weight function K is allowed to change its sign. For K in a certain weighted Lebesgue space, we prove that the antimaximum principle holds locally. A global antimaximum principle is obtained for h with compact support. For a compactly supported K, with N=1 and p=2, we provide a necessary and sufficient condition on h for the global antimaximum principle. In the course of proving our results we also establish the boundary regularity of solutions of certain boundary value problems.