Center manifolds for non-instantaneous impulsive equations under nonuniform hyperbolicity (Q784377)

The paper studies qualitative properties of a class of nonautonomous differential equations with non-instantaneous impulses under sufficiently small perturbations of the linear homogeneous part. In particular, conditions for the existence of center manifolds for this class of equations are derived under the assumption that the linear homogeneous part possesses a nonuniform exponential trichotomy. An example of a linear homogeneous differential equation with non-instantaneous impulses that is nonuniformly exponentially dichotomous is provided. The \(C^1\) smoothness of center manifolds outside the jumping time moments has been also shown.