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Global attractivity of difference equations with variable delay. (English) Zbl 0938.39016

The authors consider the difference equation with variable delay \[ x_{n+1}-x_n+p_n x_{\tau(n)}=0, \quad n=0,1,2,\cdots \] where \(\tau:\mathbb{N}\rightarrow \mathbb{Z}\), \(\tau(n)<n\) for \(n\in \mathbb{N}\), \(\lim_{n\rightarrow\infty} \tau(n)=\infty\), \(n-\tau(n)\) can be unbounded and \(\{p_n\}\) is a nonnegative sequence. Some sufficient conditions for the global attractivity of this equation are obtained.

MSC:

39A11 Stability of difference equations (MSC2000)
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