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Nonautonomous Dynamical Systems

formerly Nonautonomous and Stochastic Dynamical Systems

Editor-in-Chief: Diagana, Toka

Managing Editor: Cánovas, Jose

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Mathematical Citation Quotient (MCQ) 2015: 0.33


Emerging Science

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ISSN
2353-0626
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In This Section

Subexponential Solutions of Linear Volterra Difference Equations

Martin Bohner
  • Department of Mathematics, Missouri University of Science and Technology, Rolla, MO 65409-0020 USA
/ Nasrin Sultana
  • Department of Mathematics, Missouri University of Science and Technology, Rolla, MO 65409-0020 USA
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.

  • [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.

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

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

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

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

About the article

Received: 2015-03-05

Accepted: 2015-09-17

Published Online: 2015-10-16



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

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

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