In this paper, we study the asymptotic behavior of positive solutions of nonautonomous Beverton-Holt equation where {K n } is a positive persistent and bounded sequence. In our main result, we proved that all positive solutions {x n } satisfy the inequality The obtained result represents the extension of the Cushing-Hensons's conjecture. Applications to the case when {K n } is a positive periodic sequence are given and the alternative proof of the Cushing-Henson's conjecture is also presented.
We present an extension of Sharkovsky’s Theorem and its converse to periodic difference equations. In addition, we provide a simple method for constructing a p-periodic difference equation having an r-periodic geometric cycle with or without stability properties.
Berzelius failed to make use of Faraday's electrochemical laws in his laborious determination of equivalent weights.