Behavior of positive solutions of a difference equation. (English) Zbl 1372.39005

Tollu, D. T.; Yazlik, Y.; Taşkara, N.

J. Appl. Math. Inform. 35, No. 3-4, 217-230 (2017).

Summary: In this paper we deal with the difference equation \[ y_{n+1}\frac{ay_{n-1}}{by_ny_{n-1}+cy_{n-1}y_{n-2}+d},\, n\in\mathbb{N}_0, \] where the coefficients \(a\), \(b\), \(c\), \(d\) are positive real numbers and the initial conditions \(y_2\), \(y_1\), \(y_0\) are nonnegative real numbers. Here, we investigate global asymptotic stability, periodicity, boundedness and oscillation of positive solutions of the above equation.

MSC:

39A10	Additive difference equations
39A20	Multiplicative and other generalized difference equations, e.g., of Lyness type
39A23	Periodic solutions of difference equations

Keywords:

difference equations; global asymptotic stability; boundedness; periodic solutions; oscillation; semicycles