Oscillation of a nonlinear difference equation with several delays

Luo, X. N., Zhou, Yong, and Li, C. F.. "Oscillation of a nonlinear difference equation with several delays." Mathematica Bohemica 128.3 (2003): 309-317. <http://eudml.org/doc/249240>.

@article{Luo2003,
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, $\lbrace p_\{i\}(n)\rbrace $, $i=1,2,\dots ,m, $ is a real sequence with $p_\{i\}(n)\ge 0$ 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.},
author = {Luo, X. N., Zhou, Yong, Li, C. F.},
journal = {Mathematica Bohemica},
keywords = {nonlinear difference equtions; oscillation; eventually positive solutions; characteristic equation; nonlinear delay difference equtions; oscillation; eventually positive solutions; characteristic equation},
language = {eng},
number = {3},
pages = {309-317},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Oscillation of a nonlinear difference equation with several delays},
url = {http://eudml.org/doc/249240},
volume = {128},
year = {2003},
}

TY - JOUR
AU - Luo, X. N.
AU - Zhou, Yong
AU - Li, C. F.
TI - Oscillation of a nonlinear difference equation with several delays
JO - Mathematica Bohemica
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 128
IS - 3
SP - 309
EP - 317
AB - 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, $\lbrace p_{i}(n)\rbrace $, $i=1,2,\dots ,m, $ is a real sequence with $p_{i}(n)\ge 0$ 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.
LA - eng
KW - nonlinear difference equtions; oscillation; eventually positive solutions; characteristic equation; nonlinear delay difference equtions; oscillation; eventually positive solutions; characteristic equation
UR - http://eudml.org/doc/249240
ER -