Sharp conditions for the oscillation of delay difference equations

Ladas, G.; Philos, Ch. G.; Sficas, Y. G.

doi:10.1155/s1048953389000080

Cited by 135 publications

(54 citation statements)

References 1 publication

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“…The method of proof is similar to that of a lemma in [11] (see also the proof of Theorem 3 in [6] for the special case where /" = / for n = 0,1,...).…”

Section: I)mentioning

confidence: 99%

Oscillations in a nonautonomous delay logistic difference equation

Philos

1992

Proceedings of the Edinburgh Mathematical Society

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Consider the nonautonomous delay logistic difference equation (So) where (p n ) ng0 ' s a sequence of nonnegative numbers, (/ n ) n g 0 ' s a sequence of positive integers with lim,^,, (« -/") = oo, and K is a positive constant. Only solutions which are positive for nSO are considered. We established a sharp condition under which all solutions of (£ 0 ) are oscillatory about the equilibrium point K. Also we obtained sufficient conditions for the existence of a solution of (£ 0 ) which is nonoscillatory about K.

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“…The method of proof is similar to that of a lemma in [11] (see also the proof of Theorem 3 in [6] for the special case where /" = / for n = 0,1,...).…”

Section: I)mentioning

confidence: 99%

Oscillations in a nonautonomous delay logistic difference equation

Philos

1992

Proceedings of the Edinburgh Mathematical Society

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“…Here it should be pointed out that the following statement (see [25,28]) is correct and it should not be confused with Statement A.…”

Section: Oscillation Criteria For (1)mentioning

confidence: 94%

Oscillation Conditions for Difference Equations with a Monotone or Nonmonotone Argument

Moremedi

Stavroulakis

2018

Discrete Dynamics in Nature and Society

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Consider the first-order delay difference equation with a constant argument Δ ( ) + ( ) ( − ) = 0, = 0, 1, 2, . . . , and the delay difference equation with a variable argument Δ ( ) + ( ) ( ( )) = 0, = 0, 1, 2, . . . , where ( ) is a sequence of nonnegative real numbers, is a positive integer, Δ ( ) = ( + 1) − ( ), and ( ) is a sequence of integers such that ( ) ≤ − 1 for all ≥ 0 and lim →∞ ( ) = ∞. A survey on the oscillation of all solutions to these equations is presented. Examples illustrating the results are given.

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“…[1][2][3][4][5][6]) oscillatory behavior of solutions of difference equations and inequalities have been investigated. In this paper we study this property for solutions of the equation where q is a quotient of odd positive integers, k any fixed nonnegative integer.…”

Section: On the Oscillation Of Solutions Of Difference Equationsmentioning

confidence: 99%