Nonlinear Impulsive Differential Equations with Weighted Exponential or Ordinary Dichotomous Linear Part in a Banach Space

Abstract

We consider nonlinear impulsive differential equations with ψ-exponential and ψ-ordinary dichotomous linear part in a Banach space. By the help of Banach’s fixed-point principle sufficient conditions are found for the existence of ψ-bounded solutions of these equations on $\mathbb{R}$ and ${\mathbb{R}}_{+}$.