On solutions of the nonlinear difference equation xn+1 = f(pn,xn-2s, xn-2t-1).

In this paper, we consider a nonlinear difference equation of the form x_n+1 =f(p_n,x_n-2s,x_n-2t-1), n = 0,1,…, under some certain assumptions, where s,t ∈ {0,1,2,…} with s ⩽ t and the initial values x_-2t-1 ,x_-2t,ߪ, x₀ ∈ (0, + ∞) and p_n is the period-two sequence. We give sufficient conditions under which every positive solution of this equation converges to the period-two solution. [ABSTRACT FROM AUTHOR]