Asymptotically almost periodic solutions of limit periodic difference systems with coefficients from commutative groups
Result description
We study the behaviour of solutions of limit periodic difference systems over (infinite) fields with absolute values. The considered systems are described by the coefficient matrices that belong to commutative groups whose boundedness is not required. In particular, we are interested in special systems with solutions which vanish at infinity or which are not asymptotically almost periodic. We obtain a transparent condition on the matrix groups which ensures that the special systems form a dense subset in the space of all considered systems, i.e., that, in any neighbourhood of any considered limit periodic system, there exists a system which have non-asymptotically almost periodic or vanishing solutions. The presented results improve and extend known ones.
Keywords
limit periodicityalmost periodicitylimit periodic sequencesasymptotically almost periodic solutionsdifference equations
The result's identifiers
Result code in IS VaVaI
Result on the web
https://apcz.umk.pl/czasopisma/index.php/TMNA/article/view/TMNA.2019.051
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
Asymptotically almost periodic solutions of limit periodic difference systems with coefficients from commutative groups
Original language description
We study the behaviour of solutions of limit periodic difference systems over (infinite) fields with absolute values. The considered systems are described by the coefficient matrices that belong to commutative groups whose boundedness is not required. In particular, we are interested in special systems with solutions which vanish at infinity or which are not asymptotically almost periodic. We obtain a transparent condition on the matrix groups which ensures that the special systems form a dense subset in the space of all considered systems, i.e., that, in any neighbourhood of any considered limit periodic system, there exists a system which have non-asymptotically almost periodic or vanishing solutions. The presented results improve and extend known ones.
Czech name
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Czech description
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Classification
Type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Topological Methods in Nonlinear Analysis
ISSN
1230-3429
e-ISSN
1230-3429
Volume of the periodical
54
Issue of the periodical within the volume
2
Country of publishing house
PL - POLAND
Number of pages
21
Pages from-to
515-535
UT code for WoS article
000522656500007
EID of the result in the Scopus database
2-s2.0-85078312979
Basic information
Result type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
OECD FORD
Pure mathematics
Year of implementation
2019