IJPAM: Volume 98, No. 1 (2015)

SUFFICIENT CONDITIONS FOR OSCILLATION OF SECOND
ORDER NEUTRAL ADVANCED DIFFERENCE EQUATIONS

A. Murugesan$^1$, K. Ammamuthu$^2$
$^1$Department of Mathematics
Government Arts College (Autonomous)
Salem - 636 007, Tamil Nadu, INDIA
$^2$Department of Mathematics
Arignar Anna Government Arts College
Vadachennaimalai, Attur-636 121
Tamil Nadu, INDIA


Abstract. The aim of this paper is to study the oscillation of the second order neutral advanced difference equations \begin{equation*}\Delta(r(n)\Delta[x(n)+p(n)x(\tau(n))])+q(n)x(\sigma(n))=0,\quad n=0,1,2,....\end{equation*} Obtained results are based on the new comparison theorems that enable us to reduce problem of the oscillation of the second order equation the oscillation of the first order equations. Obtained comparison principles essentially simplify the examination of the studied equations.

Received: September 20, 2014

AMS Subject Classification: 39A10, 39A12

Key Words and Phrases: second order difference equations, neutral advanced difference equation, oscillation and nonoscillation properties

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DOI: 10.12732/ijpam.v98i1.12 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: 98
Issue: 1
Pages: 145 - 156


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