On the boundedness and local stability of

Abstract

We show that every positive solution of the difference equation in the title is bounded whenever and . This confirms a conjecture posed by Amleh et al.. We also establish local asymptotic stability properties of the difference equation.

Keywords:

• Difference equation
• Third order
• Boundedness
• Asymptotic stability

Acknowledgement

We would like to thank Gerry Ladas for suggesting this problem to us and his continuous support of our research.