Eventually vanished solutions of a forced Liénard system |
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引用本文: | 张永新.Eventually vanished solutions of a forced Liénard system[J].应用数学和力学(英文版),2009,30(10):1335-1344. |
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作者姓名: | 张永新 |
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摘 要: | In this paper, we aim to find eventually vanished solutions, a special class of bounded solutions which tend to 0 as t → ±∞), to a Lienard system with a time-dependent force. Since it is not a Hamiltonian system with small perturbations, the well-known Melnikov method is not applicable to the determination of the existence of eventually vanished solutions. We use a sequence of periodically forced systems to approximate the considered system, and find their periodic solutions. Difficulties caused by the non- Hamiltonian form are overcome by applying the Schauder's fixed point theorem. We show that the sequence of the periodic solutions has an accumulation giving an eventually vanished solution of the forced Lienard system.
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关 键 词: | 系统解 Schauder不动点定理 Melnikov方法 Liénard系统 时间依赖性 哈密顿系统 解的存在性 哈密顿形式 |
收稿时间: | 2009-04-09 |
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