Oscillation criteria of first order linear difference equations with delay argument

This paper presents new sufficient conditions for the oscillation of all proper solutions of the first order linear difference equation with delay argument Δ u ( k ) + p ( k ) u ( τ ( k ) ) = 0 , k ∈ N , where Δ u ( k ) = u ( k + 1 ) − u ( k ) , p : N → R + , τ : N → N and lim k → + ∞ τ ( k ) = + ∞...

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Bibliographic Details
Published in:Nonlinear analysis 2008-02, Vol.68 (4), p.994-1005
Main Authors: Chatzarakis, G.E., Koplatadze, R., Stavroulakis, I.P.
Format: Article
Language:English
Subjects:
Delay argument
Difference and functional equations, recurrence relations
Difference equations
Exact sciences and technology
Finite differences and functional equations
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Oscillation
Proper solution
Sciences and techniques of general use
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Summary:This paper presents new sufficient conditions for the oscillation of all proper solutions of the first order linear difference equation with delay argument Δ u ( k ) + p ( k ) u ( τ ( k ) ) = 0 , k ∈ N , where Δ u ( k ) = u ( k + 1 ) − u ( k ) , p : N → R + , τ : N → N and lim k → + ∞ τ ( k ) = + ∞ . Examples illustrating the results are given. It is to be pointed out that this is the first paper dealing with the oscillatory behaviour of the equation in the case of a general delay argument τ ( k ) .
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2006.11.055