Advances in Difference Equations | |
About reducing integro-differential equations with infinite limits of integration to systems of ordinary differential 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
【 预 览 】
Files | Size | Format | View |
---|---|---|---|
RO201904029042012ZK.pdf | 384KB | download |