Advances in Dynamical Systems and Applications
  • Year: 2006
  • Volume: 1
  • Issue: 1

On existence of positive solutions for linear difference equations with several delays

  • Author:
  • Leonid Berezansky1,, Elena Braverman2,
  • Total Page Count: 19
  • Page Number: 29 to 47

1Department of Mathematics, Ben-Gurion University of the Negev, BeerSheva 84105, Israel.

2Department of Mathematics and Statistics, University of Calgary, 2500 University Drive N.W., Calgary, AB T2N 1N4, Canada.

*Partially supported by Israeli Ministry of Absorption.

Abstract

We study the existence of positive solutions for a scalar linear difference equation with several delays:

Nonoscillation criteria, comparison theorems and some explicit nonoscillation re-sults are presented. Some known nonoscillation tests for equations with constant delays and with one variable delay are obtained as special cases.

Keywords

Linear difference equations, oscillation and nonoscillation, comparison theorems