Publication detail
Large-time behavior of a class of positive solutions of discrete equation \Delta u(n + k) = -p(n)u(n) in the critical case.
BAŠTINEC, J. DIBLÍK, J. KLIMEŠOVÁ, M.
Original Title
Large-time behavior of a class of positive solutions of discrete equation \Delta u(n + k) = -p(n)u(n) in the critical case.
Type
conference paper
Language
English
Original Abstract
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.
Keywords
discrete equation; large-time behaviour; critical case
Authors
BAŠTINEC, J.; DIBLÍK, J.; KLIMEŠOVÁ, M.
Released
21. 7. 2017
Publisher
American Institute of Physics
Location
Rhodos
ISBN
978-0-7354-1538-6
Book
International Conference on Numerical Analysis and Applied Mathematics 2016 (ICNAAM-2016)
ISBN
0094-243X
Periodical
AIP conference proceedings
State
United States of America
Pages from
480005-1
Pages to
480005-4
Pages count
4
URL