Abstract :
We consider the family of difference equations of the form
xn+1 = k
i=0
i =j,j−1
xn−i + xn−j+1xn−j + 1
k
i=0
xn−i, j= 1, 2, . . . , k,
where n ∈ {0, 1, . . .}, k ∈ {1, 2, . . .} and the initial values x−k,x−k+1, . . . , x0 are positive real numbers.
For these difference equations, we investigate the oscillatory behavior of the positive solutions
and prove that the unique equilibrium ¯x = 1 is globally asymptotically stable.
2004 Elsevier Inc. All rights reserved
