Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 0693.34073
Ruan, Jiong
Oscillatory and asymptotic behaviour of n order neutral functional differential equations. (English)
[J] Chin. Ann. Math., Ser. B 10, No.2, 143-153 (1989). ISSN 0252-9599; ISSN 1860-6261/e

The author studies the neutral functional differential equation: $$ \frac{d\sp n}{dt\sp n}[x(t)-cx(t-\tau)]+(-1)\sp{n-1}\int\sp{0}\sb{- \tau\sp*}x(t+\theta)d\eta (\theta)=0, $$ where $\tau >0$, $\tau\sp*>0$, 1-c$\ge 0$, $\eta$ ($\theta)$ is a nondecreasing bounded variational function on $[-\tau\sp*,0]$. The main results are: 1) some sufficient conditions for all solutions to be oscillatory when n is odd are otained. 2) Some sufficient conditions for all bounded solutions to be oscillating when n is even are obtained. Let $\{t\sb k,k=1,2,...,m\}$, $0>t\sb 1>t\sb 2>...>t\sb m\ge -\tau\sp*$ be a sequence in $[-\tau\sp*,0]$ and $\eta$ ($\theta)$ have positive damp on $\{t\sb k\}$, consider the equation $$ \frac{d\sp n}{dt\sp n}[x(t)-cx(t-\tau)]+(-1)\sp{n-1}\int\sp{t\sb n}\sb{t\sb 1}x(t+\theta)d\eta (\theta)=0. $$ The main results are: 1) sufficient conditions for the existence of bounded nonoscillatory solutions for all n are obtained. 2) A sufficient condition for all solutions to be oscillatory for all n is obtained.
[L.Sheng]

MSC 2000:: *34K99 Functional-differential equations
34C10 Qualitative theory of oscillations of ODE: Zeros, etc.
34E05 Asymptotic expansions (ODE)

Keywords: neutral functional differential equation; nondecreasing bounded variational function

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]