Nondegeneracy and Uniqueness of Periodic Solution for a Liénard Equation

In this paper, we consider the nondegeneracy of a Liénard equation x ′ ′ ( t ) + f ( x ( t ) ) x ′ ( t ) + a ( t ) x ( t ) = 0 . Besides, by nondegenerate results and Manásevich-Mawhin continuation theorem, we prove the existence and uniqueness of periodic solution of the related Liénard equation....

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Bibliographic Details
Published inQualitative theory of dynamical systems Vol. 21; no. 4
Main Authors Yao, Shaowen, Li, Wenjie, Cheng, Zhibo
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.12.2022
Springer Nature B.V
Subjects
Difference and Functional Equations
Dynamical Systems and Ergodic Theory
Existence theorems
Mathematics
Mathematics and Statistics
Uniqueness
34C25
Periodic solution
Liénard equation
Existence
Nondegeneracy
Uniqueness
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Summary:In this paper, we consider the nondegeneracy of a Liénard equation x ′ ′ ( t ) + f ( x ( t ) ) x ′ ( t ) + a ( t ) x ( t ) = 0 . Besides, by nondegenerate results and Manásevich-Mawhin continuation theorem, we prove the existence and uniqueness of periodic solution of the related Liénard equation.
ISSN:1575-5460
1662-3592
DOI:10.1007/s12346-022-00669-9