About reducing integro-differential equations with infinite limits of integration to systems of ordinary differential equations

Advances in Difference Equations

Alexander Domoshnitsky¹  Yakov Goltser¹ 

[1] Department of Mathematics and Computer Sciences, Ariel University of Samaria, Ariel, Israel

关键词: integro-differential equations;    fundamental matrix;    Cauchy matrix;    hyperbolic systems;   

DOI  :  10.1186/1687-1847-2013-187

学科分类：数学（综合）

来源: SpringerOpen

【 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.

【 授权许可】

CC BY