期刊名称：International Journal of Differential Equations and Applications
印刷版ISSN：1311-2872
出版年度：2000
卷号：1
期号：1
DOI：10.12732/ijdea.v1i1.205
语种：English
出版社：International Journal of Differential Equations and Applications
摘要：The present paper deals with an ordering relation for systems ODE at infinity.Some criteria for ordering (preceding or succeeding) of two systems are obtained.The proofs of the main results are based on topological principle in the theory of ODE. A relationship between (asymptotical) stability of zero solution of system ODE and introduced relation are established.We prove, that if a system generates a monotone flow then its zero solution is stable if and only if the system is preceded of zero-system ($\dot x = 0$). At the end, we prove some classical results for stability of zero solution of a given system, by the using of considered relations. The proofs are based on comparison of investigated system and a "model" system (usually zero-system).
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