Existence and uniqueness of asymptotically constant or periodic solutions in delayed population models

Abstract

By means of fixed point theory we show that the unique solution of nonlinear difference equations of the form

converges to a predetermined constant or a periodic solution. Then, we show the solution is stable and that its limit function serves as a global attractor. The same theory will be extended to two more models.

Keywords::

• nonlinear difference equations
• constant solution
• periodic solution
• contraction mapping
• global attractor

AMS Subject Classification::

• 39A10
• 34A97

Notes

^1. Email: [email protected]