IJPAM: Volume 96, No. 1 (2014)

OSCILLATION RESULTS FOR SECOND ORDER
QUASILINEAR NEUTRAL DELAY
DIFFERENTIAL EQUATIONS WITH ``MAXIMA"

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


Abstract. In this paper, some new oscillation criteria are obtained for the second order quasilinear neutral delay differential equation

\begin{displaymath}\left( a(t) \left( (x(t)+p(t)x(\tau(t)))'\right)^\alpha\right)'+q(t)\max_{[t-\sigma, t]}x^\beta(s)=0,~~t\geq t_0 \geq 0. \end{displaymath}

Some of the known results and examples are also provided to illustrate the main results. These results extend some of the known results for the equations without ``maxima".

Received: December 31, 2013

AMS Subject Classification: 34K15

Key Words and Phrases: oscillation, quasilinear, neutral, delay, differential equations with "maxima"

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DOI: 10.12732/ijpam.v96i1.1 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: 96
Issue: 1
Pages: 1 - 14


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