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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 579731, 2 pages
http://dx.doi.org/10.1155/2013/579731
Letter to the Editor

He's Max-Min Approach to a Nonlinear Oscillator with Discontinuous Terms

Department of Mathematics, Kunming University, No. 2 Puxin Road, Kunming, Yunnan 650214, China

Received 25 December 2012; Accepted 29 December 2012

Copyright © 2013 Hui-Li Zhang and Fang Xie. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Recently, the max-min approach was systematically studied in the review article (Ji-Huan, 2012). This paper concludes that He's max-min approach is also a very much effective method for nonlinear oscillators with discontinuous terms.


The ancient Chinese mathematics revives modern applications [18]; hereby, we show that He’s max-min approach [1, 911] is also very effective for nonlinear oscillators with discontinuous terms.

The max-min approach was first proposed in 2008 based on an ancient Chinese mathematics, and it has become a well-known method for nonlinear oscillators; see, for example, [1214].

To illustrate the basic idea of the max-min approach [1], we consider the following nonlinear oscillator: By a similar treatment as given in [1], we have where is the unknown frequency.

According to an ancient Chinese inequality [1, 8, 10, 11], we have where , and are constants.

According to He’s max-min approach, we set or from which the frequency can be determined approximately as which is the same as that obtained by the homotopy perturbation method [15].

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