Radial solutions for a nonlocal boundary value problem

Abstract

We consider the boundary value problem for the nonlinear Poisson equation with a nonlocal term - Δu = f(u, ∫U g(u)), u ∂U = 0. We prove the existence of a positive radial solution when f grows linearly in u, using Krasnoselskii's fixed point theorem together with eigenvalue theory. In presence of upper and lower solutions, we consider monotone approximation to solutions.