scholarly journals Gradient estimates and Harnack inequalities for nonlinear parabolic and nonlinear elliptic equations on Riemannian manifolds

1991 ◽  
Vol 100 (2) ◽  
pp. 233-256 ◽  
Author(s):  
Li Jiayu
Keyword(s):  
Riemannian Manifolds ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Gradient Estimates ◽  
Harnack Inequalities ◽  
Nonlinear Elliptic ◽  
Nonlinear Parabolic

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.

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