Abstract and Applied Analysis
Volume 2006 (2006), Article ID 38532, 11 pages
doi:10.1155/AAA/2006/38532
A nonlinear second order problem with a nonlocal boundary condition
P. Amster
and P. De Nápoli
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
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.