文章基本信息

标题：About reducing integro-differential equations with infinite limits of integration to systems of ordinary differential equations
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作者：Yakov Goltser ; 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：2013
卷号：2013
期号：1
页码：187
DOI：10.1186/1687-1847-2013-187
语种：English
出版社：Hindawi Publishing Corporation
摘要：The purpose of this paper is to propose a method for studying integro-differential equations with infinite limits of integration. The main idea of this method is to reduce integro-differential equations to auxiliary systems of ordinary differential equations. Results: a scheme of the reduction of integro-differential equations with infinite limits of integration to these auxiliary systems is described and a formula for representation of bounded solutions, based on fundamental matrices of these systems, is obtained. Conclusion: methods proposed in this paper could be a basis for the Floquet theory and studies of stability, bifurcations, parametric resonance and various boundary value problems. As examples, models of tumor-immune system interaction, hematopoiesis and plankton-nutrient interaction are considered. MSC:45J05, 45J15, 34A12, 34K05, 34K30, 47G20.
关键词：integro-differential equations ; fundamental matrix ; Cauchy matrix ; hyperbolic systems