Stable manifolds for non-instantaneous impulsive nonautonomous differential equations

Abstract

In this paper, we study stable invariant manifolds for a class of nonautonomous non-instantaneous impulsive equations where the homogeneous part has a nonuniform exponential dichotomy. We establish a stable invariant manifold result for sufficiently small perturbations by constructing stable and unstable invariant manifolds and we also show that the stable invariant manifolds are of class $C^{1}$ outside the jumping times using the continuous Fiber contraction principle technique.

Keywords

• non-instantaneous impulsive equations
• nonuniform exponential dichotomics
• invariant manifolds