Hybrid measure differential equations: existence of solutions and continuous dependence on parameters

TL;DR

This paper investigates hybrid measure differential equations, establishing the existence of various types of solutions and their continuous dependence on parameters, using fixed-point theorem extensions.

Contribution

It introduces new existence results for solutions of HMDEs and analyzes their dependence on parameters, extending fixed-point methods.

Findings

Existence of regulated, continuous, and differentiable solutions

Solutions are S-asymptotically ω-periodic

Solutions depend continuously on parameters

Abstract

This paper is devoted to study the qualitative properties of hybrid measure differential equations (HMDEs, for short). We establish several results on the existence of global solutions, including the existence of regulated, continuous, differentiable and S-asymptotically $\omega$-periodic solutions. Furthermore, we present a result on continuous dependence of solutions in terms of parameters. Our results are based on extensions of Kasnoselskii's fixed-point theorem.