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arXiv · 2501.06627

Existence and uniqueness of solution for Stieltjes differential equations with several derivators

Ignacio Márquez Albés·F. Adrián F. Tojo
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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.

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Ignacio Márquez Albés, F. Adrián F. Tojo. 2025-01-11. Existence and uniqueness of solution for Stieltjes differential equations with several derivators. https://doi.org/10.1007/s00009-021-01817-2

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