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Notes on the existence and uniqueness of solutions of Stieltjes differential equations
Author(s) -
Márquez Albés Ignacio,
Monteiro Giselle A.
Publication year - 2021
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201900138
Subject(s) - mathematics , uniqueness , monotone polygon , context (archaeology) , peano axioms , peano existence theorem , differential equation , riemann–stieltjes integral , mathematical analysis , picard–lindelöf theorem , integral equation , fixed point theorem , discrete mathematics , paleontology , geometry , danskin's theorem , biology
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.