ON SOLUTIONS OF THE RECURSIVE EQUATIONS xn+1 = xp n+1=xp n (p > 0) VIA FIBONACCI-TYPE SEQUENCES.

In this paper, by using the classical Fibonacci sequence and the golden ratio, we first give the exact solution of the nonlinear recursive equation x_n+1 = x_n-1/xn with respect to certain powers of the initial values x-1 and x0: Then we obtain a necessary and sufficient condition on the initial values for which the equation has a non-oscillatory solution. Later we extend our all results to the recursive equations xn+1 = x^p _n-1=xp n (p > 0) in a similar manner. We also get a characterization for unbounded positive solutions. At the end of the paper we analyze all possible positive solutions and display some graphical illustrations verifying our results. [ABSTRACT FROM AUTHOR]