IJPAM: Volume 72, No. 4 (2011)

OSCILLATION CRITERIA FOR EVEN ORDER
DYNAMIC EQUATIONS ON TIME-SCALES

Said R. Grace$^1$, Ravi P. Agarwal$^2$, Billûr Kaymakçalan$^3$
$^1$Department of Engineering Mathematics
Faculty of Engineering
Cairo University
Orman, Giza 12221, EGYPT
$^2$Department of Mathematics
Texas A&M University-Kingsville
Kingsville, TX 78363, USA
$^3$Department of Mathematics and Computer Science
Çankaya University
Eskişehir Yolu, 29 km, Yukarý Yurtçu, Ankara, TURKEY


Abstract. Some new criteria for the oscillation of even order linear dynamic equations on time-scales of the form

\begin{displaymath}x^{\Delta^n}(t)+q(t)x(t)=0\end{displaymath}

are established.

Received: November 18, 2011

AMS Subject Classification: 34K11, 34C10, 39A11

Key Words and Phrases: oscillation, nonoscillation, dynamic equation

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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: 72
Issue: 4