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The positive solutions of nonautonomous hyperlogistic delay difference equations

✍ Scribed by Yuji Liu; Weigao Ge

Publisher: Elsevier Science
Year: 2004
Tongue: English
Weight: 664 KB
Volume: 47
Category: Article
ISSN: 0898-1221
DOI: 10.1016/s0898-1221(04)90112-5

No coin nor oath required. For personal study only.

✦ Synopsis

Consider the nonautonomous hyperlogistic delay difference equation

where {p~} is a sequence of positive real numbers, {k~} a sequence of nonnegative integers such that {n -k=} is nondecreasing, and r a ratio of two odd integers. Our main results give sufficient conditions that guarantee every solution to be positive. The conditions under which, for all n > 1, either x~ > 1 or 0 < x~ < 1 are given, respectively. For the asymptotic behavior, we give sufficient conditions that guarantee every positive solution to converge to the equilibrium x = 1 of the model, or to oscillate about 1. The results improve and generalize some recent results established by Chen and Yu [1] and Zhou and Zhang [2]. Some remarks and examples illustrate our theorems. The methods used here are different from those in [3].

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