Eventual stability with respect to part of variables of nonlinear differential equations with non-instantaneous impulses

The eventual stability with respect to part of variables of a nonlinear differential equation with non-instantaneousimpulses is studied using Lyapunov like functions. In thesedifferential equations there are impulses, which start abruptly at somepoints and their action continue on given finite intervals.Sufficient conditions for eventual stability, uniform eventual stability andeventual asymptotic uniform stability with respect to part of variables of the zero solution are established. Examples are given to illustrate the results.