Author

Fozi M. Dannan - Saber Elaydi

Published in

Journal of mathematical analysis and applications, 143, 517-529, 1989

Abstract

In [S], the authors introduced the notion of Lipschitz stability in differential equations. This notion lies somewhere between uniform stability on one side and the notions of asymptotic stability in variation [3] and uniform stability in variation [4] on the other side. However, Lipschitz stability is new only as a nonliner phenomenon, since it coincides with uniform stability in linear systems [S]. An important feature of Lipschitz stability is that, unlike uniform stability, the linearized system inherits the property of Lipschitz stability from the original nonlinear system [5]. In this paper we pursue the study of Lipschitz stability that started in [S] using essentially the techniques of Liapunov functions. Then we give sufficient conditions for the Lipschitz stability of certain nonlinearly perturbed nonlinear systems. Such systems include, among other equations, certain integrodifferential and functional differential equations. Then we give an example which can be investigated successfully using our results but cannot be handled by any previous techniques or results [9].

Link to read full paper

https://core.ac.uk/download/pdf/82381679.pdf