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BAŠTINEC, J. DIBLÍK, J. KLIMEŠOVÁ, M.
Originální název
Large-time behavior of a class of positive solutions of discrete equation \Delta u(n + k) = -p(n)u(n) in the critical case.
Typ
článek ve sborníku ve WoS nebo Scopus
Jazyk
angličtina
Originální abstrakt
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 n\to\infty and e two-sided estimates characterizing their behavior are derived.
Klíčová slova
discrete equation; large-time behaviour; critical case
Autoři
BAŠTINEC, J.; DIBLÍK, J.; KLIMEŠOVÁ, M.
Vydáno
21. 7. 2017
Nakladatel
American Institute of Physics
Místo
Rhodos
ISBN
978-0-7354-1538-6
Kniha
International Conference on Numerical Analysis and Applied Mathematics 2016 (ICNAAM-2016)
ISSN
0094-243X
Periodikum
AIP conference proceedings
Stát
Spojené státy americké
Strany od
480005-1
Strany do
480005-4
Strany počet
4
URL
http://dx.doi.org/10.1063/1.4992641