Document Type
Article
Publication Date
2014
Publication Source
Acta Mathematica Vietnamica
Abstract
We use Lyapunov functionals to obtain sufficient conditions that guarantee exponential stability of the zero solution of the finite delay Volterra difference equation.
Also, by displaying a slightly different Lyapunov functional, we obtain conditions that guarantee the instability of the zero solution. The highlight of the paper is the relaxing of the condition |a(t)| < 1. Moreover, we provide examples in which we show that our theorems provide an improvement of some recent results.
Inclusive pages
1-13
ISBN/ISSN
0251-4184
Document Version
Postprint
Copyright
Copyright © 2014, Institute of Mathematics, Vietnam Institute of Science and Technology and Springer Science and Business Media Singapore.
Publisher
Institute of Mathematics, Vietnam Institute of Science and Technology
Peer Reviewed
yes
eCommons Citation
Kublik, Catherine and Raffoul, Youssef, "Lyapunov Functionals that Lead to Exponential Stability and Instability in Finite Delay Volterra Difference Equations" (2014). Mathematics Faculty Publications. 33.
https://ecommons.udayton.edu/mth_fac_pub/33
Comments
The version available for download after the publisher's embargo is the authors' accepted manuscript. Some differences may appear between this version and the published version. As such, it is suggested that researchers wishing to quote directly from it consult with the version of record, available online.
Permission documentation is on file.