摘要：This paper is devoted to the study of stable and unstable behaviors with growth rates e c ρ ( t ) $e^{c
ho(t)}$ for impulsive differential equations, where ρ ( t ) $
ho(t)$ is some increasing continuous function. By the techniques of impulsive analysis, we obtain the existence of stable invariant manifolds for the impulsive perturbed equation provided that the linear equation admits a ρ-nonuniform exponential dichotomy and f, g are sufficiently small Lipschitz perturbation. We also consider the case of exponential contraction and show that the asymptotic stability persists under sufficiently small nonlinear perturbations. In addition, we study how the manifolds vary with the perturbations.
