Global existence for the nonlinear heat equation in the Fujita subcritical case with initial value having zero mean value

In this paper we prove for , where k is an integer in 〚1,N〛, the existence of an initial value ψ, odd with respect to the k first coordinates, and with , such that the resulting solution of ut−Δu=|u|p−1u is global. In the case k=1 and , it is known that the solution u with the initial value u(0)=λψ blows up in finite time if λ>0 either sufficiently small or sufficiently large. The result in this paper extends a similar result of Cazenave, Dickstein, and Weissler in the case k=0, i.e. with ∫RNψ≠0 and .