## Abstract and Applied Analysis

### Periodic Solutions of Duffing Equation with an Asymmetric Nonlinearity and a Deviating Argument

#### Abstract

We study the existence of periodic solutions of the second-order differential equation ${x}^{\mathrm{\prime \prime }}+a{x}^{+}-b{x}^{-}+g\left(x\left(t-\tau \right)\right)=p\left(t\right)$, where $a,b$ are two constants satisfying $\mathrm{1}/\sqrt{a}+\mathrm{1}/\sqrt{b}=\mathrm{2}/n$, $n\in \mathrm{N}$, $\tau$ is a constant satisfying $\mathrm{0}\le \tau <\mathrm{2}\pi$, $g,p:\mathrm{R}\to \mathrm{R}$ are continuous, and $p$ is $\mathrm{2}\pi$-periodic. When the limits ${\text{lim}}_{x\to ±\mathrm{\infty }}g\left(x\right)=g\left(±\mathrm{\infty }\right)$ exist and are finite, we give some sufficient conditions for the existence of $\mathrm{2}\pi$-periodic solutions of the given equation.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 507854, 8 pages.

Dates
First available in Project Euclid: 27 February 2014

https://projecteuclid.org/euclid.aaa/1393512155

Digital Object Identifier
doi:10.1155/2013/507854

Mathematical Reviews number (MathSciNet)
MR3132543

Zentralblatt MATH identifier
1302.34104

#### Citation

Wang, Zaihong; Li, Jin; Ma, Tiantian. Periodic Solutions of Duffing Equation with an Asymmetric Nonlinearity and a Deviating Argument. Abstr. Appl. Anal. 2013 (2013), Article ID 507854, 8 pages. doi:10.1155/2013/507854. https://projecteuclid.org/euclid.aaa/1393512155

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