Odd Periodic Solutions of Fully Second-Order Ordinary Differential Equations

Yong Xiang LI, Li Juan ZHANG

Acta Mathematica Sinica, Chinese Series ›› 2022, Vol. 65 ›› Issue (2) : 287-300.

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Acta Mathematica Sinica, Chinese Series ›› 2022, Vol. 65 ›› Issue (2) : 287-300. DOI: 10.12386/A2022sxxb0022

Odd Periodic Solutions of Fully Second-Order Ordinary Differential Equations

  • Yong Xiang LI, Li Juan ZHANG
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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)),  tR
where the nonlinearity f:R3R is continuous and f(t,x,y) is 2π-periodic in t. Some existence results of odd 2π-periodic solutions are obtained under that f satisfies some precise inequality conditions. These inequality conditions allow that f(t,x,y) may be superlinear or sublinear growth on (x,y) as |(x,y)|0 and |(x,y)|.

Key words

fully second-order ODEs / odd periodic solution / Leray-Schauder fixed point theorem / cone

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Yong Xiang LI, Li Juan ZHANG. Odd Periodic Solutions of Fully Second-Order Ordinary Differential Equations. Acta Mathematica Sinica, Chinese Series, 2022, 65(2): 287-300 https://doi.org/10.12386/A2022sxxb0022

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