三阶非线性微分方程周期解的非退化和存在唯一性

数学物理学报 ›› 2022, Vol. 42 ›› Issue (2): 454-462.

三阶非线性微分方程周期解的非退化和存在唯一性

姚绍文,李文洁,程志波*()

河南理工大学数学与信息科学学院河南焦作 454003

收稿日期:2021-04-16 出版日期:2022-04-26 发布日期:2022-04-18
通讯作者: 程志波 E-mail:czb_1982@126.com
基金资助:
国家自然科学基金(11501170);河南省高校科技创新人才项目(21HASTIT025)

Nondegeneracy and Uniqueness of Periodic Solution for Third-Order Nonlinear Differential Equations

Shaowen Yao,Wenjie Li,Zhibo Cheng*()

School of Mathematics and Information Science, Henan Polytechnic University, Henan Jiaozuo 454003

Received:2021-04-16 Online:2022-04-26 Published:2022-04-18
Contact: Zhibo Cheng E-mail:czb_1982@126.com
Supported by:
the NSFC(11501170);the Scientific and Technological Innovation Talent Project for the Universities of Henan Provience(21HASTIT025)

摘要/Abstract

摘要：

该文虑了一类三阶线性微分方程 $ x'''(t)+a_{2}x''(t)+a_{1}x'(t)=a_{0}(t)x(t) $ 的非退化性. 利用Writinger不等式, 给出该方程的非退化条件.再利用三阶线性微分方程的非退化性, 证明了三阶非线性微分方程在半线性条件和超线性条件下周期解的存在唯一性.

关键词: 周期解, 非退化性, 半线性, 超线性, 存在唯一性

Abstract:

In this paper, we study the nondegeneracy of periodic solution for a third-order linear differential equation $x'''(t)+a_{2}x''(t)+a_{1}x'(t)=a_{0}(t)x(t).$ By the Writinger inequality, we give a nondegeneracy condition of the above equation. By the nondegeneracy of third-order linear differential equation, we consider the existence and uniqueness of periodic solution third-order nonlinear differential equation with semilinear and superlinear terms.

Key words: Periodic solution, Nondegeneracy, Semilinear, Superlinear, Existence and uniqueness

中图分类号:

O175.2

姚绍文,李文洁,程志波. 三阶非线性微分方程周期解的非退化和存在唯一性[J]. 数学物理学报, 2022, 42(2): 454-462.

Shaowen Yao,Wenjie Li,Zhibo Cheng. Nondegeneracy and Uniqueness of Periodic Solution for Third-Order Nonlinear Differential Equations[J]. Acta mathematica scientia,Series A, 2022, 42(2): 454-462.

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