Oscillation of High Order Neutral Delay Difference Equations with Continuous Arguments
Received:August 15, 2007  Revised:February 26, 2008
Key Word: delay difference equation   bounded solution   oscillation   nonoscillation.
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.10571050) and the Science and Research Fund for Higher College of Hunan Province (Grant No.06C054).
 Author Name Affiliation Mei HUANG Department of Mathematics and Physics, Hunan First Normal College, Hunan 410002, P. R. China Jian Hua SHEN College of Mathematics and Computer Science, Hunan Normal University, Hunan 410081, P. R. China
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In this paper, we study oscillation of solutions for a class of high order neutral delay difference equations with variable coefficients $$\Delta_\tau^m[x(t)-c(t)x(t-\tau)]=(-1)^mp(t)x(t-\sigma),~~t\geq t_0>0.$$ Some sufficient conditions are obtained for bounded oscillation of the solutions.