A sharp Liouville principle for $$\Delta _m u+u^p|\nabla u|^q\le 0$$ on geodesically complete noncompact Riemannian manifolds

2021 ◽  
Author(s):  
Yuhua Sun ◽  
Jie Xiao ◽  
Fanheng Xu
Keyword(s):  
Riemannian Manifolds ◽  
Geodesically Complete ◽  
Noncompact Riemannian Manifolds

scholarly journals Nonexistence for hyperbolic problems on Riemannian manifolds1

2020 ◽  
Vol 120 (1-2) ◽  
pp. 87-101
Author(s):  
Dario D. Monticelli ◽  
Fabio Punzo ◽  
Marco Squassina
Keyword(s):  
Euclidean Space ◽  
Riemannian Manifolds ◽  
Wave Operator ◽  
Existence Of Solutions ◽  
Necessary Conditions ◽  
Hyperbolic Problems ◽  
Power Nonlinearity ◽  
General Weight ◽  
Noncompact Riemannian Manifolds ◽  
General Weight Function

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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