Existence of solution for a nonlocal dispersal model with nonlocal term via bifurcation theory

Abstract

In this paper we study the existence of solution for the following class of nonlocal problems \[ L_0u =u \left(λ- \int_ΩQ(x,y) |u(y)|^p dy \right) , \ \mbox{in} \ Ω, \] where $Ω\subset \mathbb{R}^{N}$, $N\geq 1$, is a bounded connected open, $p>0$, $λ$ is a real parameter, $Q:Ω\times Ω\to \mathbb{R}$ is a nonnegative function, and $L_0 : C(\overlineΩ) \to (\overlineΩ)$ is a nonlocal dispersal operator. The existence of solution is obtained via bifurcation theory.