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

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 $$n \to \infty$$.

### MSC:

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

### Keywords:

global stability; linear delay difference equation
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### References:

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