On Existence of Positive Solutions for Linear Difference Equations with Several Delays

Abstract

We study the existence of positive solutions for a scalar linear difference equation with several delays: x(n + 1) x(n) = mX l=1 al(n)x(hl(n)); hl(n) n; n> n0: 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. AMS subject classication: 39A11, 39A12.