Department of Mathematics
On the asymptotic stability of volterra functional equations with vanishing delays
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.
Asymptotic stability, Vanishing delay, Volterra integral equation
Source Publication Title
Communications On Pure And Applied Analysis
American Institute of Mathematical Sciences
Brunner, Hermann, and Chunhua Ou. "On the asymptotic stability of volterra functional equations with vanishing delays." Communications On Pure And Applied Analysis 14.2 (2015): 397-406.