A nonlinear second order problem with a nonlocal boundary condition

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