## Abstract and Applied Analysis

### Infinitely Many Periodic Solutions of Duffing Equations with Singularities via Time Map

#### Abstract

We study the periodic solutions of Duffing equations with singularities ${x}^{\mathrm{\prime \prime }}+g(x)=p(t)$. By using Poincaré-Birkhoff twist theorem, we prove that the given equation possesses infinitely many positive periodic solutions provided that $g$ satisfies the singular condition and the time map related to autonomous system ${x}^{\mathrm{\prime \prime }}+g(x)=0$ tends to zero.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 398512, 8 pages.

Dates
First available in Project Euclid: 2 October 2014

https://projecteuclid.org/euclid.aaa/1412276916

Digital Object Identifier
doi:10.1155/2014/398512

Mathematical Reviews number (MathSciNet)
MR3198184

Zentralblatt MATH identifier
07022315

#### Citation

Ma, Tiantian; Wang, Zaihong. Infinitely Many Periodic Solutions of Duffing Equations with Singularities via Time Map. Abstr. Appl. Anal. 2014 (2014), Article ID 398512, 8 pages. doi:10.1155/2014/398512. https://projecteuclid.org/euclid.aaa/1412276916

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