一类受迫Liénard系统的最终零解

张永新

doi:10.3879/j.issn.1000-0887.2009.10.013

一类受迫Liénard系统的最终零解

doi: 10.3879/j.issn.1000-0887.2009.10.013

张永新

四川大学数学学院,成都 610064

详细信息

作者简介:
张永新(1976- ),男,四川三台人,讲师,博士生(E-mail:zhangyongxins@tgmail.com).

中图分类号: O175.12
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- 文章访问数: 990
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- 被引次数: 0
出版历程
- 收稿日期: 2009-04-09
- 修回日期: 2009-08-19
- 刊出日期: 2009-10-15

Eventually Vanished Solutions of a Forced Li閚ard System

ZHANG Yong-xin

Department of Mathematics, Sichuan University, Chengdu 610064, P. R. China

摘要

摘要: 寻找一类带有时间依赖强迫项的Liénard系统的最终零解，这是一种当t±∞时趋于0的特殊有界解〖CX4〗．〖CX〗由于不是微扰的Hamilton系统,所以不能使用Melnikov方法来判断最终零解的存在性．研究了一个逼近原系统的周期受迫系统序列的周期解序列，并且证明这个周期解序列有一个收敛子列，其极限就是原受迫Liénard系统的最终零解．
- 最终零解 /
- 有界解 /
- 非Hamilton系统 /
- 极限函数
Abstract: Eventually vanished solutions, a special class of bounded solutions which tend to 0→±∞, of a Linard system with a tmie-dependent force were found. Not assuming it to be a small perturbation of a Hamiltonian system, the well-known Melnikov method could not be employed to determine the existence of eventually vanished solutions. A sequence of periodically forced systems was applied to approximate the considered system and their periodic solutions were found, where the difficulties caused by the non-Hamiltonian form were overcome by applying the Schaudercs fixed point theorem. The fact that the sequence of those periodic solutions has an accumulation gave the existence of an eventually vanished solution of the forced Linard system.
- eventually vanished /
- bounded solution /
- non-Hamiltonian /
- accumu lation

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