Opuscula Math. 37, no. 6 (2017), 795-819
http://dx.doi.org/10.7494/OpMath.2017.37.6.795
Opuscula Mathematica
The second Cushing-Henson conjecture for the Beverton-Holt q-difference equation
Martin Bohner
Sabrina H. Streipert
Abstract. In this paper, we study the second Cushing-Henson conjecture for the Beverton-Holt difference equation with periodic inherent growth rate and periodic carrying capacity in the quantum calculus setting. We give a short summary of recent results regarding the Beverton-Holt difference and \(q\)-difference equation and introduce the theory of quantum calculus briefly. Next, we analyze the second Cushing-Henson conjecture. We extend recent studies in [The Beverton-Holt q-difference equation with periodic growth rate, Difference Equations, Discrete Dynamical Systems, and Applications, Springer-Verlag, Berlin, Heidelberg, New York, 2015, pp. 3-14] and state a modified formulation of the second Cushing-Henson conjecture for the Beverton-Holt \(q\)-difference equation as a generalization of existing formulations.
Keywords: Beverton-Holt equation, Cushing-Henson conjectures, \(q\)-difference equation, periodic solution.
Mathematics Subject Classification: 39A12, 39A13, 92D25.
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- Martin Bohner
- Department of Mathematics and Statistics, Missouri S&T, Rolla, MO 65409-0020, USA
- Sabrina H. Streipert
- Department of Mathematics and Statistics, Missouri S&T, Rolla, MO 65409-0020, USA
- Communicated by Marek Galewski.
- Received: 2016-07-20.
- Revised: 2017-02-12.
- Accepted: 2017-02-14.
- Published online: 2017-09-28.
