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Zbl 1106.39008
Kikina, L.K.; Stavroulakis, I.P.
A survey on the oscillation of solutions of first order delay difference equations.
(English)
[J] Cubo 7, No. 2, 223-236 (2005). ISSN 0716-7776

Authors' abstract: A survey of the most interesting results on the oscillation of all solutions of the first order delay difference equation of the form $$x_{n+1}-x_n+p_nx_{n-k}=0, \quad n=0,1,2,\dots,$$ where $\{p_n\}$ is a sequence of nonnegative real numbers and $k$ is a positive integer is presented, especially in the case when neither of the well-known oscillation conditions $$\limsup_{n\to\infty}\sum_{i=n-k}^np_i>1 \ \text { and } \ \liminf_{n\to\infty}\frac{1}{k}\sum_{i=n-k}^np_i>\frac{k^k}{(k+1)^{k+1}}$$ is satisfied.
[Jurang Yan (Taiyuan)]
MSC 2000:
*39A11 Stability of difference equations

Keywords: oscillation; nonoscillation; first order delay difference equation

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