三阶非线性微分方程周期解的非退化和存在唯一性

Abstract

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

CLC Number:

O175.2

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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References 20

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

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