## Abstract and Applied Analysis

### Boundedness of Solutions for a Class of Sublinear Reversible Oscillators with Periodic Forcing

#### Abstract

We study the boundedness of all solutions for the following differential equation ${x}^{\prime \prime }+f\left(x\right){x}^{\prime }+\left(B+\epsilon e\left(t\right)\right)|x{|}^{\alpha -\mathrm{1}}x=p\left(t\right),$ where $f\left(x\right), p\left(t\right)$ are odd functions, $e\left(t\right)$ is an even function, $e\left(t\right), p\left(t\right)$ are smooth $\mathrm{1}$-periodic functions, $B$ is a nonzero constant, and $\epsilon$ is a small parameter. A sufficient and necessary condition for the boundedness of all solutions of the above equation is established. Moreover, the existence of Aubry-Mather sets is obtained as well.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 246343, 18 pages.

Dates
First available in Project Euclid: 27 February 2014

https://projecteuclid.org/euclid.aaa/1393511928

Digital Object Identifier
doi:10.1155/2013/246343

Mathematical Reviews number (MathSciNet)
MR3065765

Zentralblatt MATH identifier
1296.34084

#### Citation

Zhang, Tingting; Si, Jianguo. Boundedness of Solutions for a Class of Sublinear Reversible Oscillators with Periodic Forcing. Abstr. Appl. Anal. 2013 (2013), Article ID 246343, 18 pages. doi:10.1155/2013/246343. https://projecteuclid.org/euclid.aaa/1393511928

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