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Existence and Uniqueness of Solution for Stieltjes Differential Equations with Several Derivators
Mediterranean Journal of Mathematics ( IF 1.1 ) Pub Date : 2021-07-12 , DOI: 10.1007/s00009-021-01817-2
Ignacio Márquez Albés 1 , F. Adrián F. Tojo 1
Affiliation  

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.



中文翻译:

多导数Stieltjes微分方程解的存在唯一性

在本文中,我们研究了微分方程组的一些存在性和唯一性结果,其中系统的每个方程都涉及不同的 Stieltjes 导数。具体来说,我们表明这个问题在 Osgood 条件下,甚至是 Montel-Tonelli 条件下只能有一个解。我们还探索了在这些条件下保证解存在的一些结果。在此过程中,我们获得了与非递减和左连续映射的有限和相关联的 Lebesgue-Stieltjes 积分的一些有趣属性,以及由此类映射定义的伪度量拓扑的表征。

更新日期:2021-07-12
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