IJPAM: Volume 70, No. 2 (2011)

OSCILLATION CRITERIA FOR 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, INDIA
$^2$Department of Mathematics
Periyar University
Salem, INDIA
$^3$Department of Mathematics
University of Tennessee at Chattanooga
Chattanooga, TN 37403, USA


Abstract. In this paper, the authors established some sufficient conditions for the oscillation of all solutions the second order nonlinear neutral delay differential equations with positive and negative coefficients

\begin{displaymath}\Big [r(t)[x(t) \pm c(t)h(x(t-\tau))]'\Big ]'+p(t)f(x(t-\delta))-q(t)g(x(t-\sigma)) = 0. \end{displaymath}

They also extended these results to certain types of forced equations. Examples illustrating the main results are given.

Received: May 14, 2011

AMS Subject Classification: 34C10, 34K11, 34K40

Key Words and Phrases: oscillation, neutral, positive and negative coefficients, Hölder's inequality

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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: 2