Boundary Value Problems
Volume 2011 (2011), Article ID 891430, 10 pages
Research Article

On a Perturbed Dirichlet Problem for a Nonlocal Differential Equation of Kirchhoff Type

Department of Mathematics, University of Messina, S. Agata, 98166 Messina, Italy

Received 24 May 2010; Accepted 26 July 2010

Academic Editor: Feliz Manuel Minhós

Copyright © 2011 Giovanni Anello. 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.


We study the existence of positive solutions to the following nonlocal boundary value problem -K(u2)Δu=λus-1+f(x,u) in Ω, u=0 on Ω, where s]1,2[, f:Ω×+ is a Carathéodory function, K:+ is a positive continuous function, and λ is a real parameter. Direct variational methods are used. In particular, the proof of the main result is based on a property of the infimum on certain spheres of the energy functional associated to problem -K(u2)Δu=λus-1 in Ω, u|Ω=0.