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Zbl 1069.39017
Thandapani, Ethiraju; Liu, Zhaoshuang; Arul, Ramalingam; Raja, Palanisamy S.
Oscillation and asymptotic behavior of second order difference equations with nonlinear neutral terms.
(English)
[J] Appl. Math. E-Notes 4, 59-67, electronic only (2004). ISSN 1607-2510/e

The authors consider second-order nonlinear neutral difference equations of the form $$\Delta(a_n\Delta(y_n-p_ny^\alpha_{n-k})) + q_nf(y_{n+1-\ell}) = 0,\ n\geq n_0\geq 0$$ with real $p$, $k>0$, $\ell\geq 0$ integers, $\alpha$ a ratio of odd positive integers, $\Delta y_n$ the forward difference, $a_n>0$ such that $\sum^\infty a_n^{-1} = \infty$, $uf(u)>0$ and $f$ is nondecreasing. Three theorems are proved: two on the oscillation of every solution and one on asymptotic stability. Some examples containing special cases of the above equation are discussed.
MSC 2000:
*39A11 Stability of difference equations
39A12 Discrete version of topics in analysis

Keywords: oscillation; asymptotic stability

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