Sharp conditions for the oscillation of delay difference equations

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

International Journal of Stochastic Analysis, 1989, vol. 2, 1-11

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.

Date: 1989
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:150178

DOI: 10.1155/S1048953389000080

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