Global asymptotic stability in a class of generalized Putnam equations

It was conjectured that for every integer m 3 the unique equilibrium c = 1 of the generalized Putnam equation xn+1 = m−2 i=0 xn−i +xn−m+1xn−m xnxn−1 + m i=2 xn−i , n= 0, 1, 2, . . . , with positive initial conditions is globally asymptotically stable. In this paper, we prove this conjecture. © 2005 Elsevier Inc. All rights reserved.