The standard Sharkovsky cycle coexistence theorem applies to impulsive differential equations: Some notes and beyond

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F19%3A73595054" target="_blank" >RIV/61989592:15310/19:73595054 - isvavai.cz</a>

Result on the web

<a href="https://obd.upol.cz/id_publ/333174940" target="_blank" >https://obd.upol.cz/id_publ/333174940</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1090/proc/14387" target="_blank" >10.1090/proc/14387</a>

Result language

angličtina

Original language name

The standard Sharkovsky cycle coexistence theorem applies to impulsive differential equations: Some notes and beyond

Original language description

We will show that, unlike usual (i.e., nonimpulsive) differential equations, the standard Sharkovsky cycle coexistence theorem applies easily to impulsive, scalar, ordinary differential equations. In fact, there is a one-to-one correspondence between the subharmonic solutions of given orders and periodic points of the same orders of the associated Poincaré translation operators, provided a uniqueness condition is satisfied. Despite the fact that the usage of the Poincaré operators in the context of impulsive differential equations is neither new, nor original, and that the application of the Sharkovsky celebrated theorem becomes in this way rather trivial, as far as we know, an appropriate theorem has not yet been formulated. As a by-product, the relationship of impulsive differential equations to deterministic chaos will also be clarified. In order to demonstrate the merit of the basic idea, some less trivial extensions for discontinuous and multivalued impulses will still be briefly done, along with indicating the situation in the lack of uniqueness.

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

S - Specificky vyzkum na vysokych skolach

Publication year

2019

Confidentiality

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

Name of the periodical

Proceedings of the American Mathematical Society

ISSN

0002-9939

e-ISSN

—

Volume of the periodical

147

Issue of the periodical within the volume

4

Country of publishing house

US - UNITED STATES

Number of pages

13

Pages from-to

1497-1509

UT code for WoS article

000458356700012

EID of the result in the Scopus database

2-s2.0-85061999002