Nonexistence for hyperbolic problems on Riemannian manifolds
classification
🧮 math.AP
keywords
hyperbolicmanifoldsnonexistencenonlinearitypowerproblemsriemannianallowed
read the original abstract
We establish necessary conditions for the existence of solutions to a class of semilinear hyperbolic problems 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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