Notes on the existence and uniqueness of solutions of Stieltjes differential equations

Ignacio Márquez Albés and Giselle A. Monteiro

Mathematische Nachrichten, 2021, vol. 294, issue 4, 794-814

Abstract: 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.

Date: 2021
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