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Existence of a nonoscillatory solution of a second-order linear neutral difference equation. (English) Zbl 1144.39004
The author considers the neutral delay difference equation with positive and negative coefficients $$\Delta^2(x_n+p x_{n-m})+p_nx_{n-k}-q_n x_{n-\ell}=0\tag1$$ where $p\in\Bbb R$ and $m,k,\ell\in\Bbb N$ and $p_n,q_n\in\Bbb R^+$, $n\ge n_0\in\Bbb N$. The main result is the following Theorem: If the conditions $$\sum^\infty ip_i<\infty,\quad \sum^\infty iq_i<\infty$$ hold, where $p\ne -1$, then equation (1) has a nonoscillatory solution.

##### MSC:
 39A11 Stability of difference equations (MSC2000) 39A10 Additive difference equations
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##### References:
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