A Final Result on the Oscillation of Solutions of the Linear Discrete Delayed Equation Δx(n)=-p(n)x(n-k) with a Positive Coefficient

A linear (k+1)th-order discrete delayed equation Δx(n)=−p(n)x(n−k) where p(n) a positive sequence is considered for n→∞. This equation is known to have a positive solution if the sequence p(n) satisfies an inequality. Our aim is to show that, in the case of the opposite inequality for p(n), all solu...

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Bibliographic Details
Published in:Abstract and Applied Analysis 2011-01, Vol.2011 (2011), p.2332-2359
Main Authors: Baštinec, J., Berezansky, L., Diblík, J., Šmarda, Z.
Format: Article
Language:English
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Summary:A linear (k+1)th-order discrete delayed equation Δx(n)=−p(n)x(n−k) where p(n) a positive sequence is considered for n→∞. This equation is known to have a positive solution if the sequence p(n) satisfies an inequality. Our aim is to show that, in the case of the opposite inequality for p(n), all solutions of the equation considered are oscillating for n→∞.
ISSN:1085-3375
1687-0409
DOI:10.1155/2011/586328