Odd Periodic Solutions of Fully Second-Order Ordinary Differential Equations with Superlinear Nonlinearities. (23rd August 2017)

• Record Type: Journal Article
• Authors: Li, Yongxiang; Guo, Lanjun
• Other Names: Liu Lishan Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2017(2017)
• Publication Date: 2017-08-23
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2017/4247365
• Languages: English
• ISSNs: 2314-8896

Abstract

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.