Abstract
The main objective of this paper is to study the boundedness character, the periodic character and the global stability of the positive solutions of the following difference equation
x(n+1) = alpha x(n) + beta x(n-1) + gamma x(n-2) + delta x(n-3) / Ax(n) + Bx(n-1) + Cx(n-2) + Dxn-3 , n = 0, 1, 2, ...
where the coefficients A, B, C, D, alpha, beta, gamma, delta, and the initial conditions x(-3), x(-2), x(-1), x(0) are arbitrary positive real numbers.