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.
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. Search in 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. 10.1017/S0308210500001761Search in 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. 10.1016/j.na.2005.11.041Search in Google Scholar
[4] M. Bohner and A. Peterson. Dynamic equations on time scales. Birkhäuser Boston Inc., Boston, MA, 2001. An introduction with applications. 10.1007/978-1-4612-0201-1Search in 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. Search in 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. Search in Google Scholar
©2015 Martin Bohner and Nasrin Sultana
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.