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-instantaneous impulses is studied using lyapunov like functions. in these differential equations there are impulses, which start abruptly at some points and their action continue on given finite intervals. sufficient conditions for eventual stability, uniform eventual stability and eventual asymptotic uniform stability with respect to part of variables of the zero solution are established. examples are given to illustrate the results.