Existence, Nonexistence and Multiplicity Results for Nonlocal Dirichlet Problems

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. © 2018 Elsevier Inc.