On the  asymptotic stability of Volterra functional equations with vanishing delays

Hermann  Brunner; Chunhua Ou

doi:10.3934/cpaa.2015.14.397

Article Contents

2015, Volume 14, Issue 2: 397-406. Doi: 10.3934/cpaa.2015.14.397

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On the asymptotic stability of Volterra functional equations with vanishing delays

Hermann Brunner^1, and
Chunhua Ou^2,

1.
Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong SAR
2.
Department of Mathematics and Statistics, Memorial University of Newfoundland, St.Johns, Newfoundland, A1C 5S7

Received: October 31, 2013

Revised: June 30, 2014

Published: February 2015

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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.

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Mathematics Subject Classification: Primary: 45M10, 34K06; Secondary: 45D99, 34E10, 34E15.

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References

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