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Zbl 1144.39004
Cheng, Jinfa
Existence of a nonoscillatory solution of a second-order linear neutral difference equation.
(English)
[J] Appl. Math. Lett. 20, No. 8, 892-899 (2007). ISSN 0893-9659

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 2000:
*39A11 Stability of difference equations
39A10 Difference equations

Keywords: nonoscillatory solution; contraction principle; neutral delay difference equation

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