On the dynamics of the nonlinear difference equation with a period-two coefficient

In this paper, we investigate the boundedness character, the periodic character and the global behavior of positive solutions of the difference equation x(n+1) = p(n)+x(n-1)^p/x(n)^p, n=0,1,... where p is positive and p(n) is a two periodic sequence of nonnegative real numbers and the initial conditions x(-1), x(0) are arbitrary positive real numbers. Morever, this paper gives an answer to Open Problem posed by Papaschinopoulos et al.