Existence, nonexistence and multiplicity results for nonlocal Dirichlet problems

Abstract

In this paper we establish various existence, nonexistence and multiplicity results for fully nonlinear Dirichlet problems associated to nonlocal Hamilton-Jacobi equations. This study is accomplished by a careful analysis of the principal eigenvalues of the elliptic operator. Resonance phenomena and anti maximum principles are also established. (C) 2018 Elsevier Inc. All rights reserved.