Radial solutions for a nonlocal boundary value problem

We consider the boundary value problem for the nonlinear Poisson equation with a nonlocal term ￠ ’ ”u=f(u, ￠ Ug(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.