  We consider a class of nonlinear integro-differential operators and prove
existence of two principal (half) eigenvalues in bounded smooth domains with
exterior Dirichlet condition. We then establish simplicity of the principal
eigenfunctions in viscosity sense, maximum principles, continuity property of
the principal eigenvalues with respect to domains etc. We also prove an
anti-maximum principle and study existence result for some nonlinear problem
via Rabinowitz bifurcation-type results.
