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
1Area 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
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.