Global stability for a class of difference equation
The authors obtain new sufficient conditions which imply that every positive solution of the equation \(x_{n+1}=(a+bx_{n})/(A+x_{n-1})\) with positive coefficients tends to a unique positive equilibrium of this equation. The theorem improves some previous results given by \textit{G.~Ladas} [Open problems and conjectures, Proc. of the 1st Int.Cconf. on Difference Equations, San Antonio, May 25-28, 1994, Gordon and Breach Publishers, 337-349 (1995; Zbl 0860.39018); J. Differ. Equ. Appl. 1, No. 3, 317-321 (1995; Zbl 0855.39006)].
scientific article; zbMATH DE number 1445599