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NEW OSCILLATION CRITERIA FOR FIRST ORDER NEUTRAL DIFFERENCE EQUATIONS

Tang Sanyi & Wang Deli (Dept. of Computer and Math., Hubei Institute for Nationalities, Enshi 445000) Xiao Yanni (Institute of Math., Academia Sinica, Beijing 100080)  
In this paper, new oscillation criteria are obtained for all solution of the firstorder neutral difference equation △(x(n) - P(n)x(n-m)) + Q(n)x(n-k) =0, n ≥n0 where m 0, k≥ 0 are integers. p(n), Q(n)∈ C({n0, n0 + 1,...}, R+). Our results do not need the usual hypothesis ∑Q(s) = ∞. Some example are given s=N to demonstrate the advantage of our results than those in the literature.
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