EUDML

In this paper we consider the nonlinear difference equation with several delays ${(a x_{n + 1} + b x_{n})}^{k} - {(c x_{n})}^{k} + \sum_{i = 1}^{m} p_{i} (n) x_{n - σ_{i}}^{k} = 0$ where $a, b, c \in (0, \infty)$ , $k = q / r, q, r$ are positive odd integers, $m$ , $σ_{i}$ are positive integers, ${p_{i} (n)}$ , $i = 1, 2, \dots, m,$ is a real sequence with $p_{i} (n) \geq 0$ for all large $n$ , and ${lim inf}_{n \to \infty} p_{i} (n) = p_{i} < \infty$ , $i = 1, 2, \dots, m$ . Some sufficient conditions for the oscillation of all solutions of the above equation are obtained.

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