IJPAM: Volume 94, No. 1 (2014)

OSCILLATORY BEHAVIOR OF THIRD ORDER
NONLINEAR NEUTRAL 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, 600 005, INDIA
$^3$MCA Department
Vel Tech. Multi Tech.
Chennai, 600032, INDIA


Abstract. In this paper, we study the oscillatory behavior of the following neutral differential equation

\begin{displaymath}[( a(t)([x(t)+p(t)x(\delta(t))])^{\prime\prime})
^\alpha]^\prime+q(t)f(x(\tau(t)))=0.\end{displaymath}

Sufficient conditions are obtained so that every every solution is either oscillatory or converges to zero. In particular. we extend the results obtained in [ 6 ] by not assuming $a(t)$ is non-decreasing. Examples are provided to illustrate the main results.

Received: October 25, 2013

AMS Subject Classification: third order, half-linear, neutral differential equation, oscillation

Key Words and Phrases: 34K11, 34C10

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DOI: 10.12732/ijpam.v94i1.6 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 94
Issue: 1
Pages: 55 - 63

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).