Boundary Value Problems
Volume 2006 (2006), Article ID 32950, 18 pages
doi:10.1155/BVP/2006/32950

Radial solutions for a nonlocal boundary value problem

Ricardo Enguiça1 and Luís Sanchez2

1Área Científica de Matemática, Instituto Superior de Engenharia de Lisboa, Rua Conselheiro Emídio Navarro, Lisboa 1-1950-062, Portugal
2Faculdade de Ciências da Universidade de Lisboa, Avenida Professor Gama Pinto 2, Lisboa 1649-003, Portugal

Received 23 August 2005; Revised 20 December 2005; Accepted 22 December 2005

Copyright © 2006 Ricardo Enguiça and Luís Sanchez. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.