IJPAM: Volume 70, No. 1 (2011)

NONOSCILLATORY SOLUTIONS OF A HIGHER-ORDER
NONLINEAR NEUTRAL DELAY DIFFERENTIAL EQUATION

Zhenyu Guo$^1$, Xiaoying Zhao$^2$, Min Liu$^3$
$^{1,2,3}$School of Sciences
Liaoning Shihua University
Fushun, Liaoning, 113001, P.R. CHINA
$^1$e-mail: guozy@163.com
$^2$e-mail: zhaoxiaoying_001@163.com
$^3$e-mail: min_liu@yeah.net


Abstract. A higher-order nonlinear neutral delay differential equation
\begin{multline*} \Big\{r_n(t)\cdots\Big[r_2(t)\big[r_1(t)[x(t)+P(t)x(t-\tau)]'\... ...ma_1),x(t-\sigma_2),\cdots,x(t-\sigma_m)\big)=0, \quad t\ge t_0, \end{multline*}
where $\tau>0,\sigma_1,\sigma_2,\cdots,\sigma_m\ge0$, $F\in C([t_0,+\infty)\times \Bbb{R}^m, \Bbb{R})$, $P,r_i\in C([t_0,\infty),\Bbb{R})$, $1\le i\le n$, is studied in this paper, and some sufficient conditions for the existence of nonoscillatory solutions of this equation are established by using Krasnoselskii fixed point theorem and expressed through five theorems according to the range of the value of the function $P(t)$.

Received: October 27, 2010

AMS Subject Classification: 34K15, 34C10

Key Words and Phrases: nonoscillatory solution, higher-order neutral delay differential equation, Krasnoselskii fixed point theorem

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 70
Issue: 1