Large-time behavior of a class of positive solutions of discrete equation Delta u(n + k) = -p(n)u(n) in the critical case.

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26220%2F17%3APU124184" target="_blank" >RIV/00216305:26220/17:PU124184 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1063/1.4992641" target="_blank" >http://dx.doi.org/10.1063/1.4992641</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1063/1.4992641" target="_blank" >10.1063/1.4992641</a>

Result language
angličtina
Original language name
Large-time behavior of a class of positive solutions of discrete equation Delta u(n + k) = -p(n)u(n) in the critical case.
Original language description
It is well-known that the discrete delayed equation Delta u(n+k)=-p_c u(n), where k is a positive integerand and p_c=frac{k^k}{(k+1)^{k+1}} has a positive solution u=u(n), n=0,1,2,dots. This is no longer true for the equation Delta u(n+k)=-pu(n) where the constant p>p_c. In the paper, the delayed discrete equation Delta (n+k)=-p^*(n)u(n) with a function p^*(n) positive for all sufficiently large n is studied. This function has a special form and satisfies the inequality p^*(n)>p_c. It is proved that, even in this case, there exists a class of positive solutions for ntoinfty and e two-sided estimates characterizing their behavior are derived.
Czech name
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Czech description
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Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
International Conference on Numerical Analysis and Applied Mathematics 2016 (ICNAAM-2016)
ISBN
978-0-7354-1538-6
ISSN
0094-243X
e-ISSN
—
Number of pages
4
Pages from-to
„480005-1“-„480005-4“
Publisher name
American Institute of Physics
Place of publication
Rhodos
Event location
Rhodos
Event date
Sep 19, 2016
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
000410159800456

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