Nonoscillatory solutions of the four-dimensional difference system

Abstract

We study asymptotic properties of nonoscillatory solutions for a four-dimensional system \[\begin{aligned} \Delta x_{n}&= C_{n}\, y_{n}^{\frac{1}{\gamma}} \\ \Delta y_{n}&= B_{n}\, z_{n}^{\frac{1}{\beta}} \\ \Delta z_{n}&= A_{n}\, w_{n}^{\frac{1}{\alpha}} \\ \Delta w_{n}&= D_{n}\, x_{n+\tau}^{\delta}. \end{aligned}\] In particular, we give sufficient conditions that any bounded nonoscillatory solution tends to zero and any unbounded nonoscillatory solution tends to infinity in all its components.

Keywords

• asymptotic properties
• difference equation
• kneser solution
• strongly monotone solution