Abstract and Applied Analysis

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

Tingting Zhang and Jianguo Si

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Abstract

We study the boundedness of all solutions for the following differential equation x + f ( x ) x + ( B + ε e ( t ) ) | x | α - 1 x = p ( t ) , where f ( x ) , p ( t ) are odd functions, e ( t ) is an even function, e ( t ) , p ( t ) are smooth 1 -periodic functions, B is a nonzero constant, and ε 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

Permanent link to this document
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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