Inserted: 19 jul 2018
Last Updated: 27 sep 2019
Journal: Asymptotic Anal.
We establish necessary conditions for the existence of solutions to a class of semilinear hyperbolic problems defined on complete noncompact Riemannian manifolds, extending some nonexistence results for the wave operator with power nonlinearity on the whole euclidean space. A general weight function depending on spacetime is allowed in front of the power nonlinearity.
Keywords: Nonexistence of solutions, hyperbolic problems, wave equation