Abstract
We consider a inhomogeneous semilinear wave equation on a noncompact complete Riemannian manifold (M, g) of dimension N >= 3, without boundary. The reaction exhibits the combined effects of a critical term and of a forcing term. Using a rescaled test function argument together with appropriate estimates, we show that the equation admits no global solution. Moreover, in the special case when M = R-3, our result improves the existing literature. Namely, our main result is valid without assuming that the initial values are compactly supported.