We study a frequently investigated class of linear difference equations with a positive coefficient and a single delay k. Recently, it was proved that if the function 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 function is bounded above and below by certain functions.
"Asymptotic Upper and Lower Estimates of a Class of Positive Solutions of a Discrete Linear Equation with a Single Delay." Abstr. Appl. Anal. 2012 (SI09) 1 - 12, 2012. https://doi.org/10.1155/2012/764351