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Notes on the existence and uniqueness of solutions of Stieltjes differential equations
Mathematische Nachrichten ( IF 1 ) Pub Date : 2021-01-29 , DOI: 10.1002/mana.201900138
Ignacio Márquez Albés 1 , Giselle A. Monteiro 2
Affiliation  

We study some classical uniqueness and existence results, such as Peano's or Osgood's uniqueness criteria, in the context of Stieltjes differential equations. This type of equation is based on derivatives with respect to monotone functions, and enables the investigation of discrete and continuous problems from a common standpoint. We compare our results with previous work on the topic and illustrate the advantages of the theorems presented in this paper with an example. Finally, we make some remarks regarding analogous uniqueness results which can be derived for measure differential equations.

中文翻译:

关于Stieltjes微分方程解的存在性和唯一性的注释

我们在Stieltjes微分方程的背景下研究了一些经典的唯一性和存在性结果,例如Peano或Osgood的唯一性标准。这种类型的方程式是基于单调函数的导数,并且可以从一个共同的角度研究离散和连续的问题。我们将我们的结果与该主题的先前工作进行了比较,并举例说明了本文中提出的定理的优势。最后,我们对可用于度量微分方程的相似唯一性结果作一些说明。
更新日期:2021-01-29
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