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.
Monticelli, D., Punzo, F., Squassina, M., Nonexistence for hyperbolic problems on Riemannian manifolds, <<ASYMPTOTIC ANALYSIS>>, 2020; (N/A): 1-15. [doi:10.3233/ASY-191580] [http://hdl.handle.net/10807/154902]
Nonexistence for hyperbolic problems on Riemannian manifolds
Squassina, Marco
2020
Abstract
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.
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