Two-Point Boundary Value Problems for a Class of Second-Order Ordinary Differential Equations

has been studied by many authors from the pioneering work of Picard 1 , who proved the existence of a solution by an application of the well-known method of successive approximations under a Lipschitz condition on g and a smallness condition on T . Sharper results were obtained by Hamel 2 in the special case of a forced pendulum equation see also 3, 4 . The existence of periodic solutions for this case has been first considered by Duffing 5 in 1918. Variational methods have been also applied when g g t, u by Lichtenstein 6 , who considered the functional