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

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.