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

We consider the N-dimensional Cauchy problem in R-N for a semilinear damped wave equation with a power-type nonlinearity vertical bar u vertical bar(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 < p <= N/[N - 2](+). This generalizes a previous result due to Todorova-Yordanov (J. Differential Equations 174 (2001) 464-489), which dealt with a solution in the framework of compactly supported initial data. (c) 2005 Elsevier Ltd. All rights reserved.