On the nonexistence of purely Stepanov almost-periodic solutions of ordinary differential equations

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F12%3A33138563" target="_blank" >RIV/61989592:15310/12:33138563 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1090/S0002-9939-2012-11154-2" target="_blank" >http://dx.doi.org/10.1090/S0002-9939-2012-11154-2</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1090/S0002-9939-2012-11154-2" target="_blank" >10.1090/S0002-9939-2012-11154-2</a>

Result language
angličtina
Original language name
On the nonexistence of purely Stepanov almost-periodic solutions of ordinary differential equations
Original language description
It is shown that in uniformly convex Banach spaces, Stepanov almost-periodic functions with Stepanov almost-periodic derivatives are uniformly almost-periodic in the sense of Bohr. This in natural situations yields, jointly with the derived properties ofthe associated Nemytskii operators, the nonexistence of purely (i.e. nonuniformly continuous) Stepanov almost-periodic solutions of ordinary differential equations. In particular, the existence problem of such solutions, considered in a series of five papers of Z. Hu and A. B. Mingarelli, is answered in a negative way.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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