On Boundedness Of Solutions Of The Difference Equation

In this paper, we study the difference equationx(n + 1) = p + x(n - 1)/x(n) , n = 0, 1, . . . ,where initial values x(-1), x(0) is an element of (0, +infinity) and 0 < p < 1, and obtain the set of all initial values (x(-1), x(0)) is an element of (0, +infinity) x (0, +infinity) such that the positive solutions {xn}(n)(infinity)=-1 are bounded. This answers the Open problem 4.8.11 proposed by Kulenovic and Ladas (Dynamics of Second Order Rational Difference Equations, with Open Problems and Conjectures, 2002).