Asymptotic Upper and Lower Estimates of a Class of Positive Solutions of a Discrete Linear Equation with a Single Delay

Abstract

We study a frequently investigated class of linear difference equationsΔv(n)=−p(n)v(n−k)with a positive coefficientp(n)and a single delayk. Recently, it was proved that if the functionp(n)is bounded above by a certain function, then there exists a positive vanishing solution of the considered equation, and the upper bound was found. Here we improve this result by finding even the lower bound for the positive solution, supposing the functionp(n)is bounded above and below by certain functions.