Abstract
This paper deals with the investigation of the following more general rational difference equation: y(n+1) = alpha y(n)/(beta+gamma Sigma(k)(i=0) y(n-(2i+1))(p) Pi(k)(i=0) y(n-(2i+1))), n = 0, 1, 2,..., where alpha, beta, gamma, p is an element of, (0, infinity) with the initial conditions x(0), x(-1) ,..., x(-2k), x(-2k-1,) is an element of (0, infinity). We investigate the existence of the equilibrium points of the considered equation and then study their local and global stability. Also, some results related to the oscillation and the permanence of the considered equation have been presented.