Measure Differential Equations with a General Nonlocal Condition

This paper is devoted to study the existence of solutions for a class of measure differential equations –abbreviated, MDEs– with a general nonlocal condition. Specifically, by a general nonlocal condition we understand a nonlocal condition modeled in terms of a multivalued map. We distinguish two cases, problems formulated in finite and infinite dimensional Banach spaces. In the first case, we formulate the problem in the context of Kurzweil-Stieltjes integrals, while for the second case we consider a Lebesgue-Stieltjes integral form. Our results are based on the fixed point theorems of Krasnoselskii and condensing multivalued maps.