Nondegeneracy and Uniqueness of Periodic Solution for a Liénard Equation

被引：0
作者：
Shaowen Yao
Wenjie Li
Zhibo Cheng
机构：
[1] Henan Polytechnic University,School of Mathematics and Information Science
来源：
Qualitative Theory of Dynamical Systems | 2022年 / 21卷
关键词：
Nondegeneracy; Uniqueness; Existence; Periodic solution; Liénard equation; 34C25.;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we consider the nondegeneracy of a Liénard equation x′′(t)+f(x(t))x′(t)+a(t)x(t)=0.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} x''(t)+f(x(t))x'(t)+a(t)x(t)=0. \end{aligned}$$\end{document}Besides, by nondegenerate results and Manásevich-Mawhin continuation theorem, we prove the existence and uniqueness of periodic solution of the related Liénard equation.
引用
收藏
相关论文
共 39 条
[1]  
Han X(2022)Positive periodic solutions to a second-order singular differential equation with indefinite weights Qual. Theory Dyn. Syst. 21 16-218
[2]  
Cheng Z(2019)Periodic solutions for a singular Liénard equation with indefinite weight Topol. Methods Nonlinear Anal. 54 203-556
[3]  
Lu S(2019)Periodic solutions for Liénard equation with an indefinite singularity Nonlinear Anal. Real World Appl. 45 542-181
[4]  
Xue R(2009)Periodic solutions for a kind of Liénard equation with a deviating argument J. Comput. Appl. Math. 228 174-234
[5]  
Lu S(2014)Periodic solutions of Liénard equation with a singularity and a deviating argument Nonlinear Anal. Real. World Appl. 16 227-787
[6]  
Guo Y(2019)Positive periodic solution to indefinite singular Liénard equation Positivity 23 779-269
[7]  
Chen L(1996)Periodic solutions of Liénard equation singular forces of repusive type J. Math. Anal. Appl. 203 254-94
[8]  
Shao J(1964)Sur les solutions Périodiques deséquations différentielles ordinaires Ann. Polo. Math. 16 69-153
[9]  
Wang J(1989)Quadratic forms, weighted eigenfunctions and boundary value problems for non-linear second order ordinary differential equations Proc. Roy. Soc. Edinburgh Sect. A 112 145-590
[10]  
Yu Y(2006)Non-degeneracy and periodic solutions of semilinear differential equations with deviation. Adv. Nonlinear Stud. 6 563-132
1234