Oscillations of difference equations with non-monotone retarded arguments

G.E. Chatzarakis and Özkan Öcalan

Applied Mathematics and Computation, 2015, vol. 258, issue C, 60-66

Abstract: Consider the first-order retarded difference equationΔx(n)+p(n)xτ(n)=0,n∈N0where (p(n))n⩾0 is a sequence of nonnegative real numbers, and (τ(n))n⩾0 is a sequence of integers such that τ(n)⩽n-1, n⩾0, and limn→∞τ(n)=∞. Under the assumption that the retarded argument is non-monotone, a new oscillation criterion, involving liminf, is established. An example illustrates the case when the result of the paper implies oscillation while previously known results fail.

Keywords: Difference equation; Non-monotone argument; Retarded argument; Oscillatory solutions; Nonoscillatory solutions (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:258:y:2015:i:c:p:60-66

DOI: 10.1016/j.amc.2015.01.110

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