IJPAM: Volume 41, No. 4 (2007)

INEQUALITIES FOR A CLASS OF POSITIVE SOLUTIONS
OF DISCRETE EQUATION $\Delta u(n+k)=-p(n)u(n)$
IN THE CRITICAL CASE

Jaromír Baštinec$^1$, Josef Diblík$^2$, Irena Hlavicková$^3$
$^{1,3}$Department of Mathematics
Faculty of Electrical Engineering and Communications
Brno University of Technology
8, Technická, Brno, 616 00, CZECH REPUBLIC
$^1$e-mail: bastinec@feec.vutbr.cz
$^3$e-mail: hlavicka@feec.vutbr.cz
$^2$Institute of Mathematics and Descriptive Geometry
Faculty of Civil Engineering
Brno University of Technology
17, Zezkova, Brno, 616 00, CZECH REPUBLIC
e-mails: diblik@feec.vutbr.cz, diblik.j@fce.vutbr.cz


Abstract.The delayed discrete equation $\Delta u(n+k)=-p(n)u(n)$ with a positive coefficient $p$ is considered. The coefficient $p$ has a special form to reflect the critical case. We prove that there exists a class of positive solutions of the above equation if $n\to \infty$ and give their estimation.

Received: October 10, 2007

AMS Subject Classification: 39A10, 39A11

Key Words and Phrases: positive solution, discrete delayed equation

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 41
Issue: 4