Abstract
We consider a inhomogeneous semilinear wave equation on a noncompact complete Riemannian manifold of dimension
, 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
, our result improves the existing literature. Namely, our main result is valid without assuming that the initial values are compactly supported.
Acknowledgments
The authors wish to thank the knowledgeable referees for the constructive remarks.
Disclosure statement
No potential conflict of interest was reported by the author(s).