Center Manifolds for Non-instantaneous Impulsive Equations Under Nonuniform Hyperbolicity

In this paper, we establish the existence of smooth center manifolds for a class of nonautonomous differential equations with non-instantaneous impulses under sufficiently small perturbations of the linear homogeneous part which has a nonuniform exponential trichotomy. In addition, we show the $C^{1}$ smoothness of center manifolds outside the jumping times.