Perron-Type Criterion for Linear Difference Equations with Distributed Delay

The characteristics of many real dynamical models are described by delay differential equations, see the list of recent papers [1–6]. However, delay differential equations are hard to manage analytically and thus many articles have examined the models by using the corresponding delay difference equations. In practice, one can easily formulate a discrete model directly by experiments or observations. For simulation purposes, nevertheless, it is important that a discrete analog faithfully inherits the characteristics of the continuous time parent system. In the recent years, the stability of solutions of linear delay difference equations has been extensively studied in the literature. Many authors have addressed this problem by using various methods and applying different techniques, see for instance the papers [7–13] and references therein. It is well known in the theory of ordinary differential equations (see, e.g., [14, page 120]) that if for every continuous function f (t) bounded on [0,∞), the solution of the equation