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Abstract and Applied Analysis
Volume 2006, Article ID 38532, 11 pages
http://dx.doi.org/10.1155/AAA/2006/38532

A nonlinear second order problem with a nonlocal boundary condition

Universidad de Buenos Aires, FCEyN, Departamento de Matemática, Ciudad Universitaria, Pabellón I, CONICET (Consejo Nacional de Investigaciones Cientí ficas y Tècnicas), Buenos Aires (1428), Argentina

Received 28 January 2005; Accepted 28 March 2005

Copyright © 2006 Hindawi Publishing Corporation. 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 study a nonlinear problem of pendulum-type for a p-Laplacian with nonlinear periodic-type boundary conditions. Using an extension of Mawhin's continuation theorem for nonlinear operators, we prove the existence of a solution under a Landesman-Lazer type condition. Moreover, using the method of upper and lower solutions, we generalize a celebrated result by Castro for the classical pendulum equation.