Odd Periodic Solutions of Fully Second-Order Ordinary Differential Equations with Superlinear Nonlinearities

This paper is concerned with the existence of periodic solutions for the fully second-order ordinary differential equation u"(t) = f(t, u(t), u'(t)), t is an element of R, where the nonlinearity f : R-3 -> R is continuous and f(t,x,y) is 2 pi-periodic in t. Under certain inequality conditions that f(t,x,y) may be superlinear growth on (x,y), an existence result of odd 2 pi-periodic solutions is obtained via Leray- Schauder fixed point theorem.