MATHEMATICA BOHEMICA, Vol. 128, No. 3, pp. 309-317 (2003)

Oscillation of a nonlinear difference equation with several delays

X. N. Luo, Yong Zhou, C. F. Li

X. N. Luo, Yong Zhou, C. F. Li, Department of Mathematics, Xiangtan University, Xiangtan, Hunan 411105, P. R. China, e-mail:

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 (MSC2000): 39A10

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