On the difference equation xn+1=alpha+xn-1/xn
In this paper we study the behavior of the solutions of the difference equation x(n)+1 = alpha + x(n)-1/x(n), n = 0, 1.... where alpha is a negative number. Included are results which considerably improve and correct those in the recently published paper: [A.E. Hamza, On the recursive sequence x(n)+1 = alpha + x(n)-1/x(n), J. Math. Anal. Appl. 322 (2006), 668-674]. We also refute Conjecture 2 in [G. Ladas, Open problems and conjectures, J. Difference. Equ. Appl. 7 (2) (2001), 477-482]. (c) 2008 Elsevier Ltd. All rights reserved.
difference equation asymptotics convergence to zero inclusion theorem period three solution