文章基本信息

标题：Homoclinic solutions for a forced generalized Liénard system
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作者：Yongxin Zhang
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2012
卷号：2012
期号：1
页码：94
DOI：10.1186/1687-1847-2012-94
语种：English
出版社：Hindawi Publishing Corporation
摘要：In this article, we find a special class of homoclinic solutions which tend to 0 as t → ± ∞ , for a forced generalized Liénard system x ¨ + f 1 ( x ) x ˙ + f 2 ( x ) x ˙ 2 + g ( x ) = p ( t ) . Since it is not a small perturbation of a Hamiltonian system, we cannot employ the well-known Melnikov method to determine the existence of homoclinic solutions. We use a sequence of periodically forced systems to approximate the considered system, and find their periodic solutions. We prove that the sequence of those periodic solutions has an accumulation which gives a homoclinic solution of the forced Liénard type system. MSC:34A34, 34C99.
关键词：homoclinic ; bounded solution ; non-Hamiltonian ; accumulation