Bifurcation of periodic solutions to nonlinear measure differential equations

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F25%3A00617745" target="_blank" >RIV/67985840:_____/25:00617745 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.21136/CMJ.2024.0120-24" target="_blank" >https://doi.org/10.21136/CMJ.2024.0120-24</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.21136/CMJ.2024.0120-24" target="_blank" >10.21136/CMJ.2024.0120-24</a>

Result language

angličtina

Original language name

Bifurcation of periodic solutions to nonlinear measure differential equations

Original language description

The paper is devoted to the periodic bifurcation problems for generalizations of ordinary differential systems. The bifurcation is understood in the static sense of Krasnoselskiĭ and Zabreĭko. First, the conditions necessary for the given point to be bifurcation point for non autonomous generalized ordinary differential equations (based on the Kurzweil gauge type generalized integral) are proved. Then, as the main contribution, analogous results are obtained also for the nonlinear non autonomous measure differential equations considered in the sense of distributions. To this aim their relationship to Kurzweil's generalized differential equations is disclosed. Although the measure differential equations turned out to be special cases of those Kurzweil's equations, the proofs of the main results of the paper are by no means the straightforward consequences of the analogous results for generalized differential equations. Essentially they rely on the theory of the Kurzweil-Stieltjes integration. It is worth noting that as the systems studied in the paper encompass many types of equations such as impulsive differential equations, ordinary differential equations, dynamic equations on time scales etc., the results of the paper offer applications to rather wide scale of practical problems. Two illustrating examples are included, as well.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10101 - Pure mathematics

Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2025

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Czechoslovak Mathematical Journal

ISSN

0011-4642

e-ISSN

1572-9141

Volume of the periodical

75

Issue of the periodical within the volume

1

Country of publishing house

DE - GERMANY

Number of pages

38

Pages from-to

357-395

UT code for WoS article

001410568700001

EID of the result in the Scopus database

2-s2.0-105001092408