Periodic solutions of discrete Volterra equations

Baker, Christopher and Song, Yihong (2004) Periodic solutions of discrete Volterra equations. Mathematics and Computers in Simulation, 64 (5). pp. 521-542. ISSN 0378-4754

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Abstract

In this paper, we investigate periodic solutions of linear and nonlinear discrete Volterra equations of convolution or non-convolution type with unbounded memory. For linear discrete Volterra equations of convolution type, we establish Fredholm’s alternative theorem and for equations of non-convolution type, and we prove that a unique periodic solution exists for a particular bounded initial function under appropriate conditions. Further, this unique periodic solution attracts all other solutions with bounded initial function. All solutions of linear discrete Volterra equations with bounded initial functions are asymptotically periodic under certain conditions. A condition for periodic solutions in the nonlinear case is established. © 2003 IMACS. Published by Elsevier B.V. All rights reserved.

Item Type:	Article
Uncontrolled Keywords:	Periodic; Asymptotically periodic solutions; Discrete Volterra equations; Resolvent matrices; Fredholm’s alternative
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User:	Ms Lucy van Russelt
Date Deposited:	12 Nov 2007
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/874

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