Global existence of solutions for semilinear damped wave equations in RN with noncompactly supported initial data

We consider the N-dimensional Cauchy problem in RN for a semilinear damped wave equation with a power-type nonlinearity |u|p. For a noncompactly supported initial data, which has a small energy, we shall derive a global in time existence result in the case when the power of the nonlinear term satisfies 1+2/N