*(English)*Zbl 1198.39028

The authors investigate global stability and asymptotic behavior of solutions of the system of two difference equations

where $B,C$ are positive real constants. The papers by *S. Stević* [Discrete Dyn. Nat. Soc. 2007, Article ID 87519, 10 p. (2007; Zbl 1180.39004)] and by *D. C. Zhang* and *B. Shi* [J. Math. Anal. Appl. 278, No. 1, 194–202 (2003; Zbl 1025.39013)], where *one* equation of the above form is investigated, serve as a motivation. A typical result of the paper is the following statement.

**Theorem.**

A detailed analysis of the solvability of the nonlinear algebraic system describing the equilibria of the investigated system of the two difference equations play an important role in the proofs of the authors’ statements.

##### MSC:

39A30 | Stability theory (difference equations) |

39A22 | Growth, boundedness, comparison of solutions (difference equations) |

39A10 | Additive difference equations |