Global stability of a linear nonautonomous delay difference equation. (English) Zbl 0855.39007

Erbe, L. H.; Xia, H.

J. Difference Equ. Appl. 1, No. 2, 151-161 (1995).

The authors study the global stability of the linear delay difference equation (*) \(x_{n + 1} - x_n + p_n x_{n - k} = 0\), where \(\{p_n\}\) is a sequence of nonnegative real numbers and \(k \geq 0\) is an integer. In fact they prove the following Theorem: Assume that \(\sum^\infty_{n = 0} p_n = \infty\) and \(\mu \equiv \limsup_{n \to \infty} \sum^\infty_{i = n - k} p_i < 3/2 + 1/2 (k + 1)\). Then every solution of equation (*) tends to zero as \(n \to \infty\).

Reviewer: P.Talpalaru (Iaşi)

MSC:

39A11	Stability of difference equations (MSC2000)
39A10	Additive difference equations

Keywords:

global stability; linear delay difference equation

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