Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (1): 131-138.

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Positive Periodic Solutions for a Damped Duffing Equation with Singularity of Attractive Type

Chenyang Xia,Zhenhui Wang*(),Zhibo Cheng   

  1. School of Mathematics and Information Science, Henan Polytechnic University, Henan Jiaozuo 454003
  • Received:2021-03-23 Online:2022-02-26 Published:2022-02-23
  • Contact: Zhenhui Wang E-mail:tiantian@hpu.edu.com
  • Supported by:
    the NSFC(11501170);the Scientific and Technological Innovation Talent Project for the Universities of Henan Provience(21HASTIT025)

Abstract:

In this paper, we consider a damped Duffing equation with singularity of attractive type where $C$ is a constant and $C\neq0$, $g$ is a continuous function and has an attractive singularity at $u=0$. By applications of Manasevich-Mawhin continuation theorem and some analysis skill, we establish some sufficient conditions for the existence of positive $T$-periodic solutions for this equation.

Key words: Duffing equation, Manasevich-Mawhin theorem, Singularity of attractive type, Strong and weak singular, Positive periodic solution

CLC Number: 

  • O175.1
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