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

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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.

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Acknowledgements

Ignacio Márquez Albés was partially supported by Xunta de Galicia under grant ED481A-2017/095 and project ED431C 2019/02. F. Adrián F. Tojo was partially supported by Xunta de Galicia, project ED431C 2019/02, and by the Agencia Estatal de Investigación (AEI) of Spain under Grant MTM2016-75140-P, co-financed by the European Community fund FEDER.

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  1. Departamento de Estatística, Facultade de Matemáticas, Análise Matemática e Optimización Instituto de Matemáticas, Universidade de Santiago de Compostela, Campus Vida, 15782, Santiago, Spain

    Ignacio Márquez Albés & F. Adrián F. Tojo

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  1. Ignacio Márquez Albés
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  2. F. Adrián F. Tojo
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Correspondence to Ignacio Márquez Albés.

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Albés, I.M., Tojo, F.A.F. Existence and Uniqueness of Solution for Stieltjes Differential Equations with Several Derivators. Mediterr. J. Math. 18, 181 (2021). https://doi.org/10.1007/s00009-021-01817-2

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  • DOI: https://doi.org/10.1007/s00009-021-01817-2

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