About reducing integrodifferential equations with infinite limits of integration to systems of ordinary differential equations
 Yakov Goltser,
 Alexander Domoshnitsky
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Abstract
The purpose of this paper is to propose a method for studying integrodifferential equations with infinite limits of integration. The main idea of this method is to reduce integrodifferential equations to auxiliary systems of ordinary differential equations.
Results: a scheme of the reduction of integrodifferential 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 tumorimmune system interaction, hematopoiesis and planktonnutrient interaction are considered.
MSC: 45J05, 45J15, 34A12, 34K05, 34K30, 47G20.
Inside
Within this Article
 1 Introduction
 2 Methods: about bounded solutions of linear nonhomogeneous systems
 3 Results: about reduction of integrodifferential equations to systems of ordinary differential equations
 4 Results: examples of reduction of integrodifferential equations to systems of ordinary differential equations
 5 Results: systems with advanced argument
 6 Results: about systems with both delayed and advanced argument
 7 Conclusions
 References
 References
Other actions
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 Title
 About reducing integrodifferential equations with infinite limits of integration to systems of ordinary differential equations
 Open Access
 Available under Open Access This content is freely available online to anyone, anywhere at any time.
 Journal

Advances in Difference Equations
2013:187
 Online Date
 June 2013
 DOI
 10.1186/168718472013187
 Online ISSN
 16871847
 Publisher
 Springer International Publishing
 Additional Links
 Topics
 Keywords

 integrodifferential equations
 fundamental matrix
 Cauchy matrix
 hyperbolic systems
 Authors

 Yakov Goltser ^{(3)}
 Alexander Domoshnitsky ^{(3)}
 Author Affiliations

 3. Department of Mathematics and Computer Sciences, Ariel University of Samaria, Ariel, Israel