Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

On the asymptotic stability of volterra functional equations with vanishing delays

Language

English

Abstract

We analyze the asymptotic stability of solutions of linear Volterra integral equations with general continuous convolution kernels and vanishing delays. The analysis is based on an extension of the variation-of-parameter formula for non-delay Volterra integral equations and on energy function techniques. The delay integral equations studied in this paper will be of interest in the (still open) stability analysis of numerical methods (e.g. collocation and Runge-Kutta-type methods) for Volterra integral equations with vanishing delays.

Keywords

Asymptotic stability, Vanishing delay, Volterra integral equation

Publication Date

2015

Source Publication Title

Communications On Pure And Applied Analysis

Volume

14

Issue

2

Start Page

397

End Page

406

Publisher

American Institute of Mathematical Sciences

DOI

10.3934/cpaa.2015.14.397

Link to Publisher's Edition

http://dx.doi.org/10.3934/cpaa.2015.14.397

ISSN (print)

15340392

ISSN (electronic)

15535258

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