Periodic solutions of ordinary differential equations with bounded nonlinearities - Ward, James Robert (Topological Methods in Nonlinear Analysis, 2002)
In this article we discuss the existence and non-existence of forced T-periodic solutions to ordinary differential equations of the form u^′ ′ +g(u)=e(t). The results concern equations with bounded nonlinear terms g satisfying g(s)> 0 (or g(s)< 0) for all real numbers s, and g(± ∞ )=0. Variational and topological methods are employed.