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Notes on the existence and uniqueness of solutions of Stieltjes differential equations. (English) Zbl 07746479

Summary: 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.
{© 2021 Wiley-VCH GmbH}

MSC:

26A24 Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
34A36 Discontinuous ordinary differential equations
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