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Nonautonomous Dynamical Systems

formerly Nonautonomous and Stochastic Dynamical Systems

Editor-in-Chief: Diagana, Toka

Managing Editor: Cánovas, Jose


Mathematical Citation Quotient (MCQ) 2017: 0.71

Open Access
Online
ISSN
2353-0626
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Subexponential Solutions of Linear Volterra Difference Equations

Martin Bohner
  • Department of Mathematics, Missouri University of Science and Technology, Rolla, MO 65409-0020 USA
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Nasrin Sultana
  • Department of Mathematics, Missouri University of Science and Technology, Rolla, MO 65409-0020 USA
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2015-10-16 | DOI: https://doi.org/10.1515/msds-2015-0005

Abstract

We study the asymptotic behavior of the solutions of a scalar convolution sum-difference equation. The rate of convergence of the solution is found by determining the asymptotic behavior of the solution of the transient renewal equation.

Keywords: Subexponential; transient renewal; convolutions; Banach space; linear operator

References

  • [1] Ravi P. Agarwal. Difference equations and inequalities, volume 228 of Monographs and Textbooks in Pure and Applied Mathematics. Marcel Dekker Inc., New York, second edition, 2000. Theory, methods, and applications. Google Scholar

  • [2] John A. D. Appleby and David W. Reynolds. Subexponential solutions of linear integro-differential equations and transient renewal equations. Proc. Roy. Soc. Edinburgh Sect. A, 132(3):521–543, 2002. Google Scholar

  • [3] Cezar Avramescu and Cristian Vladimirescu. On the existence of asymptotically stable solutions of certain integral equations. Nonlinear Anal., 66(2):472–483, 2007. Google Scholar

  • [4] M. Bohner and A. Peterson. Dynamic equations on time scales. Birkhäuser Boston Inc., Boston, MA, 2001. An introduction with applications. Google Scholar

  • [5] Theodore Allen Burton. Volterra integral and differential equations, volume 167 of Mathematics in Science and Engineering. Academic Press Inc., Orlando, FL, 1983. Google Scholar

  • [6] Walter G. Kelley and Allan C. Peterson. Difference equations. Harcourt/Academic Press, San Diego, CA, second edition, 2001. An introduction with applications. Google Scholar

About the article

Received: 2015-03-05

Accepted: 2015-09-17

Published Online: 2015-10-16


Citation Information: Nonautonomous Dynamical Systems, Volume 2, Issue 1, ISSN (Online) 2353-0626, DOI: https://doi.org/10.1515/msds-2015-0005.

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©2015 Martin Bohner and Nasrin Sultana. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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[1]
Małgorzata Migda and Janusz Migda
Electronic Journal of Qualitative Theory of Differential Equations, 2018, Number 3, Page 1

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