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,∫Ug(u)), u|∂U=0. We prove the existence of a positive radial solution when f grows linearly in u, using Krasnoselskiiés fixed point theorem together with eigenvalue theory. In presence of upper and lower solutions, we consider monotone approximation to solutions.