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Zbl 1224.39018
Rath, R.N.; Misra, N.; Rath, S.K.
Sufficient conditions for oscillatory behaviour of a first order neutral difference equation with oscillating coefficients. (English)
[J] Acta Math. Acad. Paedagog. Nyházi. (N.S.) 25, No. 1, 55-63 (2009). ISSN 1786-0091/e

Summary: We obtain sufficient conditions so that every solution of neutral functional difference equation $$ \Delta(y_n - p_n y_{\tau(n)}) + q_n G(y_{\sigma(n)}) = f_n$$ oscillates or tends to zero as $n\to \infty$. Here, $\Delta$ is the forward difference operator given by $\Delta x_n = x_{n+1}-x_n$, and $p_n$, $q_n$, $f_n$ are the terms of oscillating infinite sequences; $\{\tau_n\}$ and $\{\sigma_n\}$ are non-decreasing sequences, which are less than $n$ and approaches $\infty$ as $n$ approaches $\infty$. This paper generalizes and improves some recent results.

MSC 2000:: *39A21
39A10 Difference equations
39A12 Discrete version of topics in analysis
39A22
34K40 Neutral equations
34K11 Oscillation theory of functional-differential equations

Keywords: oscillation; asymptotic behavior; neutral functional difference equation

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