Existence and Uniqueness of Solution for Stieltjes Differential Equations with Several Derivators

Abstract

In this paper, we study some existence and uniqueness results for systems of differential equations in which each of the equations of the system involves a different Stieltjes derivative. Specifically, we show that this problems can only have one solution under the Osgood condition, or even, the Montel–Tonelli condition. We also explore some results guaranteeing the existence of solution under these conditions. Along the way, we obtain some interesting properties for the Lebesgue–Stieltjes integral associated with a finite sum of nondecreasing and left-continuous maps, as well as a characterization of the pseudometric topologies defined by this type of maps.