In this paper we prove for , where k is an integer in , the existence of an initial value ψ, odd with respect to the k first coordinates, and with , such that the resulting solution of is global. In the case and , it is known that the solution u with the initial value blows up in finite time if either sufficiently small or sufficiently large. The result in this paper extends a similar result of Cazenave, Dickstein, and Weissler in the case , i.e. with and .