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Far East Journal of Applied Mathematics

Far East Journal of Applied Mathematics
Volume 95, Issue 4, Pages 229 - 247 (October 2016)
http://dx.doi.org/10.17654/AM095040229

NECESSARY AND SUFFICIENT CONDITIONS FOR OSCILLATIONS OF HIGHER ORDER NEUTRAL DIFFERENCE EQUATIONS WITH SEVERAL DELAYS

A. Murugesan and P. Sowmiya

Abstract:

Consider the mth order neutral delay difference equation

(*)

where is a positive integer, are positive integers with and We establish necessary and sufficient conditions for oscillation of solutions of the equation (*) for the cases m is odd and m is even. Our results have straightforward extension for advanced difference equations.