Existence and non-existence results for a class of semilinear nonlocal operators with exterior condition

Abstract

We consider a class of semilinear nonlocal problems with vanishing exterior condition and establish a Ambrosetti-Prodi type phenomenon when the nonlinear term satisfies certain conditions. Our technique makes use of the probabilistic tools and heat kernel estimates.

arXiv admin note: text overlap with arXiv:1803.08540