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Oscillation and nonoscillation of neutral difference equations with positive and negative coefficients

✍ Scribed by X.H. Tang; J.S. Yu; D.H. Peng

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 489 KB
Volume: 39
Category: Article
ISSN: 0898-1221
DOI: 10.1016/s0898-1221(00)00073-0

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✦ Synopsis

In this paper, we investigate the oscillation and nonoscillation of the neutral difference equation with variable coefficients

where pn,qn, c~n (n = 0,1,2,...) are real numbers with pn >_ 0, qn >_ 0, cn _> 0, k, l, and r are integers with 0 < I < k -1, r > 0, Pn -qn-k+l ~--0, and not identically zero. Several new sufficient conditions for the oscillation of all solutions of equation ( .) are established, some of them are "sharp". Our results do not need the usual hypothesis oo (p. -= oo n=0

and improve the all known results in the literature. The existence theorems for the positive solutions are also obtained. ~

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