Uniqueness of harmonic mappings and of solutions of elliptic equations on Riemannian manifolds

1979 ◽  
Vol 240 (3) ◽  
pp. 231-250 ◽  
Author(s):  
Willi J�ger ◽  
Helmut Kaul
Keyword(s):  
Riemannian Manifolds ◽  
Elliptic Equations ◽  
Harmonic Mappings

MULTIPLE SOLUTIONS FOR NONLINEAR ELLIPTIC EQUATIONS ON COMPACT RIEMANNIAN MANIFOLDS

2007 ◽  
Vol 18 (09) ◽  
pp. 1071-1111 ◽  
Author(s):  
JÉRÔME VÉTOIS
Keyword(s):  
Continuous Function ◽  
Riemannian Manifolds ◽  
Elliptic Equations ◽  
Multiple Solutions ◽  
Nonlinear Elliptic Equations ◽  
Beltrami Operator ◽  
Hölder Continuous ◽  
Nonlinear Elliptic

Let (M,g) be a smooth compact Riemannian n-manifold, n ≥ 4, and h be a Holdër continuous function on M. We prove multiplicity of changing sign solutions for equations like Δg u + hu = |u|2* - 2 u, where Δg is the Laplace–Beltrami operator and 2* = 2n/(n - 2) is critical from the Sobolev viewpoint.

Blow-up solutions for asymptotically critical elliptic equations on Riemannian manifolds

2009 ◽  
Vol 58 (4) ◽  
pp. 1719-1746 ◽  
Author(s):  
Anna Maria Micheletti ◽  
Angela Pistoia ◽  
Jerome Vetois
Keyword(s):  
Riemannian Manifolds ◽  
Elliptic Equations ◽  
Blow Up
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