Odd Periodic Solutions of Fully Second-Order Ordinary Differential Equations with Superlinear Nonlinearities. (23rd August 2017) - Li, Yongxiang; Guo, Lanjun
Abstract : 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 ∈ R, where the nonlinearity f : R 3 → R is continuous and f ( t, x, y ) is 2 π -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 π -periodic solutions is obtained via Leray-Schauder fixed point theorem.