Subexponential Solutions of Linear Volterra Difference Equations

Martin Bohner; Nasrin Sultana

Nonautonomous Dynamical Systems (2015)

  • Volume: 2, Issue: 1, page 63-76, electronic only
  • ISSN: 2353-0626

Abstract

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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.

How to cite

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Martin Bohner, and Nasrin Sultana. "Subexponential Solutions of Linear Volterra Difference Equations." Nonautonomous Dynamical Systems 2.1 (2015): 63-76, electronic only. <http://eudml.org/doc/276534>.

@article{MartinBohner2015,
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.},
author = {Martin Bohner, Nasrin Sultana},
journal = {Nonautonomous Dynamical Systems},
keywords = {Subexponential; transient renewal; convolutions; Banach space; linear operator; subexponential},
language = {eng},
number = {1},
pages = {63-76, electronic only},
title = {Subexponential Solutions of Linear Volterra Difference Equations},
url = {http://eudml.org/doc/276534},
volume = {2},
year = {2015},
}

TY - JOUR
AU - Martin Bohner
AU - Nasrin Sultana
TI - Subexponential Solutions of Linear Volterra Difference Equations
JO - Nonautonomous Dynamical Systems
PY - 2015
VL - 2
IS - 1
SP - 63
EP - 76, electronic only
AB - 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.
LA - eng
KW - Subexponential; transient renewal; convolutions; Banach space; linear operator; subexponential
UR - http://eudml.org/doc/276534
ER -

References

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  1. [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. [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.  Zbl1009.45007
  3. [3] Cezar Avramescu and Cristian Vladimirescu. On the existence of asymptotically stable solutions of certain integral equations. Nonlinear Anal., 66(2):472–483, 2007.  Zbl1110.45004
  4. [4] M. Bohner and A. Peterson. Dynamic equations on time scales. Birkhäuser Boston Inc., Boston, MA, 2001. An introduction with applications.  Zbl0978.39001
  5. [5] Theodore Allen Burton. Volterra integral and differential equations, volume 167 of Mathematics in Science and Engineering. Academic Press Inc., Orlando, FL, 1983.  
  6. [6] Walter G. Kelley and Allan C. Peterson. Difference equations. Harcourt/Academic Press, San Diego, CA, second edition, 2001. An introduction with applications.  Zbl0970.39001

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