Abstract
Nonlinear differential equations with non-instantaneous impulses are studied. The impulses start abruptly at some points and their actions continue on given finite intervals. We pursue the study of Lipschitz stability using Lyapunov functions. Some sufficient conditions for Lipschitz stability, uniform Lipschitz stability, and uniform global Lipschitz stability are obtained. Examples are given to illustrate the results.
Highlights
1 Introduction The problems of stability of solutions of differential equations via Lyapunov functions have been successfully investigated in the past
Remark Note in some papers the functions of non-instantaneous impulses are given in the form gk(t, x(t)), i.e. they do not depend on the value of the solution before the jump x(sk – )
We study the Lipschitz stability using the following scalar comparison differential equation with non-instantaneous impulses:
Summary
The problems of stability of solutions of differential equations via Lyapunov functions have been successfully investigated in the past. In this paper Lipschitz stability of solutions of nonlinear non-instantaneous impulsive differential equations is defined and studied. Lipschitz stability of impulsive functional-differential equations is studied in [ ].
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