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Oscillation Criteria for First Order Delay Difference Equations

Authors:	Ioannis P.?Stavroulakis author-information" > author-information__contact u-icon-before" > mailto:ipstav@cc.uoi.gr" title=" ipstav@cc.uoi.gr" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author

Affiliation:	(1) Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece

Abstract:	Oscillation criteria for all solutions of the first order delay difference equation of the form $x_{n+1}- x_{n} + p_nx_{n-k} = 0, quad n = 0, 1, 2,...,$ where {p_n} is a sequence of nonnegative real numbers and k is a positive integer are established especially in the case that the well-known oscillation conditions $limsup_{nrightarrow infty} sum^n_{i=n-k} p_i > 1 quad and quad liminf_{nrightarrow infty} {1over k} sum^{n-1}_{i=n-k} p_i > {k^kover (k+1)^{k+1}}$ are not satisfied.Dedicated to Professor Y.G. Sficas on the occasion of his 60h birthday

Keywords:	39A11
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