Oscillation of higher-order delay difference equations.
Zhou, Yinggao (2006)
Advances in Difference Equations [electronic only]
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Zhou, Yinggao (2006)
Advances in Difference Equations [electronic only]
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Raafat Abo-Zeid (2014)
Mathematica Bohemica
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In this paper, we determine the forbidden set and give an explicit formula for the solutions of the difference equation where , , are positive real numbers and the initial conditions , , are real numbers. We show that every admissible solution of that equation converges to zero if either or with . When with , we prove that every admissible solution is unbounded. Finally, when , we prove that every admissible solution converges to zero.
Ocalan, Ozkan (2006)
Portugaliae Mathematica. Nova Série
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Pavel Jahoda, Monika Jahodová (2008)
Acta Mathematica Universitatis Ostraviensis
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Let be the set of prime numbers (or more generally a set of pairwise co-prime elements). Let us denote , where . Then for arbitrary finite set , holds and If we denote where is the set of all prime numbers, then for closure of set holds where .