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Optimal oscillation
criteria for first order difference equations with delay
argument
George E. Chatzarakis, Roman Koplatadze and Ioannis P. Stavroulakis |
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Vol. 235 (2008), No. 1, 15–33
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Abstract |
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Consider the first order linear difference equation  where Δu(k) = u(k + 1) − u(k), p : N → ℝ+, τ : N → N, τ(k) ≤ k − 2 and limk→+∞τ(k) = +∞. Optimal conditions for the oscillation of all proper solutions of this equation are established. The results lead to a sharp oscillation condition, when k − τ(k) → +∞ as k → +∞. Examples illustrating the results are given. |
Keywords
difference equation, proper solution, positive solution,
oscillatory
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Mathematical Subject Classification 2000
Primary: 39A11
Secondary: 39A12
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Milestones
Received: 30 May 2007
Revised: 10 July 2007
Accepted: 11 October 2007
Published: 1 March 2008
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Authors |
| George E. Chatzarakis | |
| Department of Mathematics University of Ioannina 451 10 Ioannina Greece |
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| Roman Koplatadze | |
| Department of Mathematics University of Tbilisi University Street 2 Tbilisi 0143 Georgia |
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| Ioannis P. Stavroulakis | |
| Department of Mathematics University of Ioannina 451 10 Ioannina Greece |
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