Fredholm alternative for the p-Laplacian in higher dimensions

Abstract

In this paper we characterize the set of all right-hand sides h ∈ C(ΒΩ) for which the boundary value problem ? has at least one weak solution u ∈ WO1,p (Ω). Here 1 < p < 2, and λ1 > 0 is the first eigenvalue of the p-Laplacian. In particular, we prove that for ∫Ωh1 = 0 this problem is solvable and the energy functional is unbounded from below. © 2001 Academic Press.