Periodic solutions for a class of second-order ordinary differential equations

This paper is devoted to the study of periodic solutions for a class of second-order ordinary differential equations by utilizing a technique for obtaining solutions to free problems in the calculus of variations originating in the work of Caratheodory (Ref. 1, 1935). The key of this technique is to find some suitable transformation which transfers the periodic solution problem to an equivalent variational problem in which the minimizer is more easily determined. Some applications are presented to illustrate the utility of this technique.