IJPAM: Volume 77, No. 3 (2012)

OSCILLATION OF THIRD ORDER HALF LINEAR
NEUTRAL DELAY DIFFERENTIAL EQUATIONS

E. Thandapani$^1$, S. Tamilvanan$^2$, E.S. Jambulingam$^3$
$^{1,2}$Ramanujan Institute for Advanced Study in Mathematics
University of Madras
Chennai, 600005, INDIA
$^3$MCA Department
Vel Tech Multi Tech
Chennai, 600032, INDIA


Abstract. This paper is concerned with the oscillatory behavior of third order neutral differential equation

\begin{displaymath}[a(t)([x(t) + p(t)x(\delta(t))]^{\prime\prime})^\alpha]^\prime + q(t)x^\alpha(\sigma(t)) = 0, \quad t\geq t_0, \eqno(E)
\end{displaymath}

where $a(t),p(t)$, and $q(t)$ are positive functions, $\alpha>0$ is a quotient of odd positive integers, and $\sigma(t)\leq t$, $\delta(t)\leq t$.

Some new oscillation criteria for equation (E) are established. Examples illustrating the main results are included.

Received: December 19, 2011

AMS Subject Classification: 34K11

Key Words and Phrases: third order, half-linear, neutral delay differential equation, oscillation, nonoscillation

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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: 77
Issue: 3