Global attractivity of the equilibrium of for q < p
Date of Original Version
We investigate the global attractivity of the equilibrium of second-order difference equation xn+1 = pxn + xn-1/qx n + xn-1, n = 0, 1,... where the parameters p, q, q < p and initial conditions x-1, x0 are nonnegative for all n . We prove that the unique equilibrium of this equation is global attractor which gives the affirmative answer to a conjecture of Kulenović and Ladas. The method of proof is innovative, and it has the potential to be used in the proof of global attractivity of equilibria of many similar equations.
Journal of Difference Equations and Applications
Kulenović, M. R.S., and Orlando Merino. "Global attractivity of the equilibrium of for q < p." Journal of Difference Equations and Applications 12, 1 (2006): 101-108. doi:10.1080/10236190500410109.