Table of Contents Author Guidelines Submit a Manuscript
International Journal of Mathematics and Mathematical Sciences
Volume 19, Issue 3, Pages 435-440
http://dx.doi.org/10.1155/S0161171296000622

Cone valued Lyapunov functions and Lipschitz stability of nonlinear systems of differential equations

Crawford Science Hall, Bowie State University, Bowie 20715, MD, USA

Received 4 October 1994

Copyright © 1996 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We introduce a new comparison result which will be an important tool when we apply cone valued Lyapunov like functions. We also introduce new concepts of ϕ0-uniform Lipschitz stability and (λ,λ,ϕ0)-practical stability and employ our comparison result to carry out stability analysis of nonlinear systems. Our results are also applicable to nonlinear perturbed systems.