Positive periodic solutions for discrete population models. (English) Zbl 1053.39027

Zhang, Guang; Cheng, Sui Sun

Nonlinear Funct. Anal. Appl. 8, No. 3, 335-344 (2003).

The authors study delay discrete population models of the form \[ x(n+1)=a(n)x(n)+\lambda h(n)f(x(n-\tau(n))), \;n\in \mathbb{Z}, \tag{E} \] where \(\{a(n)\}_{n\in \mathbb{Z}}\) and \(\{h(n)\}_{n\in \mathbb{Z}}\) are positive \(\omega\)-periodic sequences, \(\{\tau(n)\}_{n\in \mathbb{Z}}\) is an integer valued \(\omega\)-periodic sequence and \(\lambda\) is a positive parameter. By using Krasnosel’skij’s fixed point theorem, some existence criteria are established for the periodic solutions of the equation (E).

Reviewer: Wei Nian Li (Shanghai)

MSC:

39A11	Stability of difference equations (MSC2000)
92D25	Population dynamics (general)

Keywords:

difference equation; periodic solution; delay discrete population models; Krasnosel’skij’s fixed point theorem