IJPAM: Volume 64, No. 1 (2010)

CLASSIFICATION OF SOLUTIONS OF SECOND ORDER
NONLINEAR NEUTRAL DELAY DIFFERENTIAL EQUATIONS
WITH POSITIVE AND NEGATIVE COEFFICIENTS

E. Thandapani$^1$, V. Muthulakshmi$^2$, John R. Graef$^3$
$^1$Ramanujan Institute for Advanced Study in Mathematics
University of Madras
Chennai, 600005, INDIA
e-mail: [email protected]
$^2$Department of Mathematics
Periyar University
Salem, 636 011, INDIA
e-mail: [email protected]
$^3$Department of Mathematics
The University of Tennessee at Chattanooga
Chattanooga, TN 37403-2598, USA
e-mail: [email protected]


Abstract.The oscillatory and nonoscillatory behavior of solutions of the nonlinear neutral differential equation \begin{equation*}
\Big [r(t)[x(t)+c(t)x(t-\tau)]'\Big ]'+p(t)f(x(t-\delta))-q(t)g(x(t-\sigma))
= 0,
\end{equation*} where $c$, $r$, $p$, $q \in C([t_0,\infty),\mathbb{R})$, $f$, $g \in C(\mathbb{R},\mathbb{R})$, and $\tau$, $\delta$, $\sigma \in \mathbb{R}_+$, are studied. Examples illustrating the relevance of the results are given.

Received: September 10, 2010

AMS Subject Classification: 34C10, 34C15, 34K10

Key Words and Phrases: delay differential equation, neutral equation, positive and negative coefficients, oscillation, second order

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 64
Issue: 1