Existence and uniqueness of solution for Stieltjes differential equations with several derivators
Classical Analysis and ODEs
2025-01-14 v1
Abstract
In this paper, we study some existence and uniqueness results for systems of differential equations in which each of 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 to a finite sum of nondecreasing and left-continuous maps, as well as a characterization of the pseudometric topologies defined by this type of maps.
Keywords
Cite
@article{arxiv.2501.06627,
title = {Existence and uniqueness of solution for Stieltjes differential equations with several derivators},
author = {Ignacio Márquez Albés and F. Adrián F. Tojo},
journal= {arXiv preprint arXiv:2501.06627},
year = {2025}
}