Stability With Respect to Part of Variables of Nonlinear Differential Equations with Non-Instantaneous Impulses

摘要

Nonlinear differential equations with non-instantaneous impulses are studied. In these differential equations we have impulses, which start abruptly at some points and their action continue on given finite intervals. The stability with respect to part of variables of a nonlinear differential equation with non-instantaneous impulses is studied using Lyapunov like functions. Sufficient conditions for stability, uniform stability and asymptotic uniform stability with respect to part of variables of the zero solution are established. Examples are given to illustrate the results.