2007.135: Periodic solutions of discrete Volterra equations
2007.135: Christopher Baker and Yihong Song (2004) Periodic solutions of discrete Volterra equations. Mathematics and Computers in Simulation, 64 (5). pp. 521-542. ISSN 0378-4754
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DOI: 10.1016/j.matcom.2003.10.002
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 2000 > 65 Numerical analysis |
| MIMS number: | 2007.135 |
| Deposited By: | Mrs Louise Healey |
| Deposited On: | 12 November 2007 |
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