IJPAM: Volume 104, No. 2 (2015)

OSCILLATION OF SECOND ORDER NEUTRAL
DIFFERENTIAL EQUATIONS WITH MIXED NEUTRAL TERM

R. Arul$^1$, V.S. Shobha$^2$
$^{1,2}$Department of Mathematics
Kandaswami Kandar's College
Velur - 638 182, Namakkal Dt.
Tamil Nadu, INDIA


Abstract. This paper deals with the following second order neutral differential equation of the form

\begin{displaymath}(r(t)z'(t))'+q(t)x(\sigma(t))=0,~~t\geq t_0 \geq 0\end{displaymath}

where $z(t)=x(t)+a(t)x(t-\tau)+b(t)x(t+\delta),$ and $~\int_{t_0}^{\infty}\frac{1}{r(t)}dt=\infty$. We obtain some new oscillation criteria which extend some known results. Examples are presented to illustrate the main results.

Received: April 22, 2015

AMS Subject Classification: 34K11

Key Words and Phrases: second order, neutral differential equation, mixed neutral term, oscillation

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DOI: 10.12732/ijpam.v104i2.3 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: 2015
Volume: 104
Issue: 2
Pages: 181 - 191


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