An Ambrosetti-Prodi type result for integral equations involving dispersal operator

In this paper we study the existence of solution for the following class of nonlocal problems \[ L_0u =f(x,u)+g(x) , \ in \ Ω, \] where Ω⊂ RN, N≥ 1, is a bounded connected open, g ∈ C(Ω), f:Ω × R → R are function, and L₀ : C(Ω) → C(Ω) is a nonlocal dispersal operator. Using a sub-supersolution method and the degree theory for $γ$-Condensing maps, we have obtained a result of the Ambrosetti-Prodi type, that is, we obtain a necessary condition on g for the non-existence of solutions, the existence of at least one solution, and the existence of at least two distinct solutions.