具有非线性导数项的二阶常微分方程的正周期解

Journal of Jilin University Science Edition ›› 2023, Vol. 61 ›› Issue (6): 1243-1250.

Positive Periodic Solutions of Second-Order Ordinary Differential Equations with Nonlinear Derivative Terms

LIU Xiaoming, LI Yongxiang

College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Received:2023-03-23 Online:2023-11-26 Published:2023-11-26

Abstract

Abstract: We discuss the existence of positive 2π-periodic solutions of the second-order ordinary differential equation with nonlinear derivative term by using positive operator perturbation method and fixed point index theory in cones. Under certain inequality conditions of the
nonlinear term f(t,x,y), we obtain the existence of positive 2π-periodic solutions of the equation.

Key words: second-order ordinary differential equation, nonlinear derivative term, positive 2π-periodic solution, closed convex cone, fixed point index

CLC Number:

O175.14

LIU Xiaoming, LI Yongxiang. Positive Periodic Solutions of Second-Order Ordinary Differential Equations with Nonlinear Derivative Terms[J].Journal of Jilin University Science Edition, 2023, 61(6): 1243-1250.

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Positive Periodic Solutions of Second-Order Ordinary Differential Equations with Nonlinear Derivative Terms

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