Analytical solution of a rational difference equationA. Khaliq, S. HassanWe have studied some qualitative properties such as boundedness of solutions, stability character and periodic nature of the third-order rational difference equationzn+1 = δ +1/znzn-1zn-2, n=0,1,... with parameter δ and with arbitrary initial conditions for which the denominator is always positive. It is worth to mention that our problem is a natural extension of the Open Problem 8.2 and confirm the Conjecture 8.1 declared by A.M. Amleh, E. Camouzis and G. Ladas in On the Dynamics of a Rational Difference Equations I (International Journal of Difference Equations, Volume 3, Number 1, 2008, pp. 1-35). |
Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 15(1) (2022), pp. 181-202