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

In this paper we study the existence of solution for the following class of nonlocal problems $$L_{0}u=u(\lambda -{\int }_{\mathrm{\Omega }}Q(x,y)\mathrm{\mid }u(y){\mathrm{\mid }}^{p}dy),in\mathrm{\Omega },$$ where $\mathrm{\Omega }\subset {\mathbb{R}}^N$, $N\ge 1$, is a bounded connected open, $p>0$, $\lambda$ is a real parameter, $Q:\mathrm{\Omega }\times \mathrm{\Omega }\to \mathbb{R}$ is a nonnegative function, and $L_0 : C(\overline{\Omega}) \to (\overline{\Omega})$ is a nonlocal dispersal operator. The existence of solution is obtained via bifurcation theory.