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Sharp conditions for the oscillation of delay difference equations

Author

Listed:
  • G. Ladas
  • Ch. G. Philos
  • Y. G. Sficas

Abstract

Suppose that { p n } is a nonnegative sequence of real numbers and let k be a positive integer. We prove that lim n → ∞ inf  [ 1 k ∑ i = n − k n − 1 p i ] > k k ( k + 1 ) k + 1 is a sufficient condition for the oscillation of all solutions of the delay difference equation A n + 1 − A n + p n A n − k = 0 ,    n = 0 , 1 , 2 , … . This result is sharp in that the lower bound k k / ( k + 1 ) k + 1 in the condition cannot be improved. Some results on difference inequalities and the existence of positive solutions are also presented.

Suggested Citation

  • G. Ladas & Ch. G. Philos & Y. G. Sficas, 1989. "Sharp conditions for the oscillation of delay difference equations," International Journal of Stochastic Analysis, Hindawi, vol. 2, pages 1-11, January.
    • Handle: RePEc:hin:jnijsa:150178
    DOI: 10.1155/S1048953389000080
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    Cited by:

    1. Bolat, Yaşar, 2009. "Oscillation of higher order neutral type nonlinear difference equations with forcing terms," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2973-2980.
    2. Karpuz, Başak & Özsavaş, Büşra, 2021. "An improved product type oscillation test for partial difference equations," Applied Mathematics and Computation, Elsevier, vol. 391(C).

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