Oscillation of second order nonlinear neutral delay difference equations. (English) Zbl 1035.34074
Summary: We obtain sufficient conditions for the oscillation of all solutions to the second-order nonlinear delay difference equation
\[
\Delta[a_n(\Delta(x_n+p_nx_{g(n)}))^{\alpha}]+f(n,x_{\sigma(n)})=0,
\]
where \(\Delta x_n=x_{n+1}-x_n\) is the forward difference operator, \(\{p_n\}\) is a sequence of nonnegative real numbers and \(\alpha \geqslant 1\) is a quotient of positive odd integers. Our results extend and improve some known results in the literature. An example that dwell up the advantage of our results is included.
MSC:
| 34K11 | Oscillation theory of functional-differential equations |
| 34K40 | Neutral functional-differential equations |
References:
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