Oscillation analysis for nonlinear difference equation with non-monotone arguments. (English) Zbl 1446.39013
Summary: The aim of this paper is to obtain some new oscillatory conditions for all solutions of nonlinear difference equation with non-monotone or non-decreasing argument
\[
\Delta x(n)+p(n)f \bigl( x \bigl( \tau (n) \bigr) \bigr) =0,\quad n=0,1,\dots ,
\]
where \((p(n)) \) is a sequence of nonnegative real numbers and \((\tau (n)) \) is a non-monotone or non-decreasing sequence, \(f\in C(\mathbb{R},\mathbb{R})\) and \(xf(x)>0\) for \(x\neq 0\).
MSC:
| 39A21 | Oscillation theory for difference equations |
| 39A22 | Growth, boundedness, comparison of solutions to difference equations |
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