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

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.