文章基本信息

标题：An Extension of the Invariance Principle for a Class of Differential Equations with Finite Delay
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作者：Marcos Rabelo ; L. F. C. Alberto
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2010
卷号：2010
期号：1
页码：496936
DOI：10.1155/2010/496936
语种：English
出版社：Hindawi Publishing Corporation
摘要：An extension of the uniform invariance principle for ordinary differential equations with finite delay is developed. The uniform invariance principle allows the derivative of the auxiliary scalar function to be positive in some bounded sets of the state space while the classical invariance principle assumes that . As a consequence, the uniform invariance principle can deal with a larger class of problems. The main difficulty to prove an invariance principle for functional differential equations is the fact that flows are defined on an infinite dimensional space and, in such spaces, bounded solutions may not be precompact. This difficulty is overcome by imposing the vector field taking bounded sets into bounded sets.
关键词：Lipschitzian Function ; Chaotic Attractor ; Global Attractor ; Functional Differential Equation ; Invariance Principle