Geodesic
Oscillation of forced nonlinear neutral delay difference equations of first order
Czechoslovak Mathematical Journal, Tome 53 (2003) no. 1, pp. 83-101 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Necessary and sufficient conditions are obtained for every solution of \[ \Delta (y_{n}+p_{n}y_{n-m})\pm q_{n}G(y_{n-k})=f_{n} \] to oscillate or tend to zero as $n\rightarrow \infty $, where $p_{n}$, $q_{n}$ and $f_{n}$ are sequences of real numbers such that $q_{n}\ge 0$. Different ranges for $p_{n}$ are considered.
Necessary and sufficient conditions are obtained for every solution of \[ \Delta (y_{n}+p_{n}y_{n-m})\pm q_{n}G(y_{n-k})=f_{n} \] to oscillate or tend to zero as $n\rightarrow \infty $, where $p_{n}$, $q_{n}$ and $f_{n}$ are sequences of real numbers such that $q_{n}\ge 0$. Different ranges for $p_{n}$ are considered.
Classification : 39A10, 39A11, 39A12
Keywords: neutral difference equations; oscillation; nonoscillation; asymptotic behaviour 
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Parhi, N.; Tripathy, A. K. Oscillation of forced nonlinear neutral delay difference equations of first order. Czechoslovak Mathematical Journal, Tome 53 (2003) no. 1, pp. 83-101. http://geodesic.mathdoc.fr/item/CMJ_2003_53_1_a7/

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