文章基本信息

标题：Differential Inequalities for One Component of Solution Vector for Systems of Linear Functional Differential Equations
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作者：Alexander Domoshnitsky
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：478020
DOI：10.1155/2010/478020
语种：English
出版社：Hindawi Publishing Corporation
摘要：The method to compare only one component of the solution vector of linear functional differential systems, which does not require heavy sign restrictions on their coefficients, is proposed in this paper. Necessary and sufficient conditions of the positivity of elements in a corresponding row of Green's matrix are obtained in the form of theorems about differential inequalities. The main idea of our approach is to construct a first order functional differential equation for the th component of the solution vector and then to use assertions about positivity of its Green's functions. This demonstrates the importance to study scalar equations written in a general operator form, where only properties of the operators and not their forms are assumed. It should be also noted that the sufficient conditions, obtained in this paper, cannot be improved in a corresponding sense and does not require any smallness of the interval , where the system is considered.
关键词：Ordinary Differential Equation ; Differential System ; Approximate Method ; Delay System ; Functional Differential Equation