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

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