The Picard-Lindelöf Theorem and continuation of solutions for measure differential equations

Gastón Beltritti; Stefania Demaria; Graciela Giubergia; Fernando Mazzone

Czechoslovak Mathematical Journal (2025)

  • Issue: 1, page 47-68
  • ISSN: 0011-4642

Abstract

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We obtain, by means of Banach's Fixed Point Theorem, convergence for the Picard iterations associated to a general nonlinear system of measure differential equations. We study the existence of left-continuous solutions defined on maximal intervals and we establish some properties of these maximal solutions.

How to cite

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Beltritti, Gastón, et al. "The Picard-Lindelöf Theorem and continuation of solutions for measure differential equations." Czechoslovak Mathematical Journal (2025): 47-68. <http://eudml.org/doc/299930>.

@article{Beltritti2025,
abstract = {We obtain, by means of Banach's Fixed Point Theorem, convergence for the Picard iterations associated to a general nonlinear system of measure differential equations. We study the existence of left-continuous solutions defined on maximal intervals and we establish some properties of these maximal solutions.},
author = {Beltritti, Gastón, Demaria, Stefania, Giubergia, Graciela, Mazzone, Fernando},
journal = {Czechoslovak Mathematical Journal},
keywords = {measure differential equation; Lebesgue-Stieltjes integral; fixed point theory; maximal solution},
language = {eng},
number = {1},
pages = {47-68},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The Picard-Lindelöf Theorem and continuation of solutions for measure differential equations},
url = {http://eudml.org/doc/299930},
year = {2025},
}

TY - JOUR
AU - Beltritti, Gastón
AU - Demaria, Stefania
AU - Giubergia, Graciela
AU - Mazzone, Fernando
TI - The Picard-Lindelöf Theorem and continuation of solutions for measure differential equations
JO - Czechoslovak Mathematical Journal
PY - 2025
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 1
SP - 47
EP - 68
AB - We obtain, by means of Banach's Fixed Point Theorem, convergence for the Picard iterations associated to a general nonlinear system of measure differential equations. We study the existence of left-continuous solutions defined on maximal intervals and we establish some properties of these maximal solutions.
LA - eng
KW - measure differential equation; Lebesgue-Stieltjes integral; fixed point theory; maximal solution
UR - http://eudml.org/doc/299930
ER -

References

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