Existence and uniqueness of solution for Stieltjes differential equations with several derivators
type: Item
instance of: scholarly article
title: Existence and uniqueness of solution for Stieltjes differential equations with several derivators
zbMATH Open document ID: 1485.34010
author: Ignacio Márquez Albés
author: F. Adrián F. Tojo
published in: Mediterranean Journal of Mathematics
publication date: 2021-08-30T00:00:00Z
review text: The paper deals with systems of nonlinear first-order Stieltjes differential equations of the form \[ (x_i)'_{g_i}(t)=f_i(t,x(t)),\quad i\in\{1,\ldots,n\}, \] in which each component \(x_i\) is being differentiated with respect to a different derivator \(g_i\) (a nondecreasing and left-continuous function). The authors consider initial-value problems for this type of systems, and establish analogues of the Osgood uniqueness theorem, Montel-Tonelli uniqueness theorem, as well as sufficient conditions for the existence of solutions.
reviewed by: Antonín Slavík
Mathematics Subject Classification ID: 34A06
Mathematics Subject Classification ID: 34A12
zbMATH DE Number: 7388021
zbMATH Keywords: Stieltjes differential equation
zbMATH Keywords: Stieltjes derivative
zbMATH Keywords: uniqueness
zbMATH Keywords: existence
MaRDI profile type: Publication
full work available at URL: s00009-021-01817-2
OpenAlex ID: W3181135291
Wikidata QID: Q115390255
cites work: Measure Theory and Probability Theory
cites work: Q3438773
cites work: Measure functional differential equations and functional dynamic equations on time scales
cites work: Stieltjes Bochner spaces and applications to the study of parabolic equations
cites work: Theory and applications of first-order systems of Stieltjes differential equations
cites work: Stieltjes differential systems with nonmonotonic derivators
cites work: Q5719499
cites work: A new unification of continuous, discrete and impulsive calculus through Stieltjes derivatives
cites work: General existence principles for Stieltjes differential equations with applications to mathematical biology
cites work: Systems of Stieltjes differential equations with several derivators
cites work: Existence of extremal solutions for discontinuous Stieltjes differential equations
cites work: Extremal solutions of systems of measure differential equations and applications in the study of Stieltjes differential problems
cites work: Solvability of non-semicontinuous systems of Stieltjes differential inclusions and equations
cites work: Notes on the existence and uniqueness of solutions of Stieltjes differential equations
cites work: Distributional, differential and integral problems: equivalence and existence results
cites work: Extremal solutions for measure differential inclusions via Stieltjes derivatives
cites work: Kurzweil–Stieltjes Integral
cites work: Q5817554
cites work: Q4340161
cites work: Periodic boundary value problems involving Stieltjes derivatives
cites work: Q4353856
cites work: Q4023958
cites work: Transformations of Lebesgue-Stieltjes integrals
DOI: 10.1007/S00009-021-01817-2
description: scientific article; zbMATH DE number 7388021