Regulated solutions for nonlinear measure driven equations

We obtain the existence of regulated solutions for measure integral equations driven by a nondecreasing function, thus modeling a large class of hybrid systems (without any restriction on their Zeno behavior). By working with Kurzweil–Stieltjes integrals and making use of a measure of noncompactness, we are able to avoid Lipschitz-type assumptions. We finally present very useful particular cases and further applications of our result.