zbMATH — the first resource for mathematics

A periodically forced Beverton-Holt equation. (English) Zbl 1023.39013
The authors present an open problem: to prove or disprove the following assertions for \(p\geq 3\).
(a) The periodically forced Beverton-Holt equation \[ x_{n+1}=\frac{rK_n}{K_n+(r-1)x_n}x_n, \quad n=0, 1, 2, \ldots, \] has a positive \(p\)-periodic solution \(\{y_n\}\), and it is globally attracting for \(x_0>0\), where \(r>1\) and \(\{K_n\}\) is a sequence of positive numbers with a base period \(p\geq 1\).
(b) If \(p>2\), the strict inequality \(av(y_n)<av(K_n)\) holds. Here \(av(y_n)=\frac{1}{p}\sum_{i=0}^{p-1}y_i\).

39B05 General theory of functional equations and inequalities
39A11 Stability of difference equations (MSC2000)
Full Text: DOI
[1] DOI: 10.1080/10236190108808308 · Zbl 1002.39003 · doi:10.1080/10236190108808308
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.