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Oscillation and asymptotic behavior of second order difference equations with nonlinear neutral terms. (English) Zbl 1069.39017
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.

39A11Stability of difference equations (MSC2000)
39A12Discrete version of topics in analysis
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