X. N. Luo, Yong Zhou, C. F. Li, Department of Mathematics, Xiangtan University, Xiangtan, Hunan 411105, P. R. China, e-mail: yzhou@xtu.edu.cn
Abstract: In this paper we consider the nonlinear difference equation with several delays
(ax_{n+1}+bx_n)^k-(cx_n)^k+\sum\limits_{i=1}^m p_i(n)x^k_{n-\sigma_i}=0
where $a,b,c\in(0,\infty)$, $k=q/r, q, r$ are positive odd integers, $m$, $\sigma_i$ are positive integers, $\{p_i(n)\}$, $i=1,2,\dots,m, $ is a real sequence with $p_i(n)\geq0$ for all large $n$, and $\liminf_{n\rightarrow\infty}p_i(n)=p_i<\infty$, $i=1,2,\dots,m$. Some sufficient conditions for the oscillation of all solutions of the above equation are obtained.
Keywords: nonlinear difference equtions, oscillation, eventually positive solutions, characteristic equation
Classification (MSC 2000): 39A10
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