一类带阻尼的吸引型奇性Duffing方程周期正解的存在性

Abstract

Abstract:

In this paper, we consider a damped Duffing equation with singularity of attractive type $u''(t)+Cu'(t)+g(u(t))=e(t), $ 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

Chenyang Xia,Zhenhui Wang,Zhibo Cheng. Positive Periodic Solutions for a Damped Duffing Equation with Singularity of Attractive Type[J].Acta mathematica scientia,Series A, 2022, 42(1): 131-138.

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References 16

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

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