Existence of solutions for semilinear measure driven equations

The paper investigates existence of solutions for abstract semilinear measure driven equations in Banach spaces. This general system can model a large class of hybrid systems without any restriction on their Zeno behavior. An existence criterion for the system is obtained by using Schauder's fixed point theorem. When reducing to nonlinear measure driven system, we present some new or less restrictive criteria than those in the literature in the sense of Lebesgue–Stieltjes integral. Finally, an example is given to illustrate our results.