IJPAM: Volume 75, No. 4 (2012)


Tongxing Li$^1$, Ethiraju Thandapani$^2$, John R. Graef$^3$
$^1$School of Control Science and Engineering
Shandong University
Jinan, Shandong 250061, P.R. CHINA
$^1$School of Mathematical Science
University of Jinan
Shandong, 250022, P.R. CHINA
$^2$Ramanujan Institute For Advanced Study in Mathematics
University of Madras
Chennai 600005, INDIA
$^3$Department of Mathematics
The University of Tennessee at Chattanooga
Chattanooga, TN 37403-2598, USA

Abstract. This paper is concerned with the oscillatory and asymptotic behavior of the solutions of the third-order neutral retarded differential equation \begin{equation*}
\left[a(t)\left(b(t)\left(x(t) + p(t)x(t-\tau)\right)'\right)'\right]'+q(t)x(t-\sigma)=0,
\end{equation*}where $a(t)>0$, $b(t)>0$, $q(t)\geq0$, $0\leq p(t) <1$, and $\sigma>\tau\geq0$. Examples illustrating the main result are given.

Received: January 20, 2012

AMS Subject Classification: 34C10, 34K11

Key Words and Phrases: third-order, neutral retarded differential equation, oscillation

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 75
Issue: 4