IJPAM: Volume 87, No. 2 (2013)

OSCILLATION CRITERIA FOR SECOND ORDER
NEUTRAL DIFFERENCE EQUATIONS WITH
NEGATIVE NEUTRAL TERM

E. Thandapani$^1$, V. Balasubramanian$^2$, John R. Graef$^3$
$^1$Ramanujan Institute For Advanced Study in Mathematics
University of Madras
Chennai, 600005, INDIA
$^2$Department of Mathematics
Periyar University
Salem, 636 011, INDIA
$^3$Department of Mathematics
University of Tennessee at Chattanooga
Chattanooga, TN 37403, USA


Abstract. In this paper the authors obtain some new results on the oscillatory behavior of second order neutral difference equations of the form

\begin{displaymath}\Delta \Big(a_n (\Delta (x_n -p_n x_{n-\tau}))^\alpha \Big) + q_n f(x_{n-\sigma})=0, \end{displaymath}

where $0\leq p_n\leq p<1$, $q_n>0$, and $\alpha$ is a ratio of odd positive integers. Examples are provided to illustrate the main results.

Received: April 9, 2013

AMS Subject Classification: 39A11

Key Words and Phrases: second order, nonlinear, neutral difference equation, oscillation, negative neutral term

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DOI: 10.12732/ijpam.v87i2.9 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: 2013
Volume: 87
Issue: 2