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On the number of nodal solutions for a nonlinear elliptic problem on symmetric Riemannian manifolds
RiemannianManifolds Nodal Solutions Topological Meth-ods
2011/2/28
We consider the problem −"2gu+u = |u|p−2u in M, where (M, g) is a symmetric Riemannian manifold. We give a multiplicity result for antisymmetric changing sign solutions.
A maximum rank problem for degenerate elliptic fully nonlinear equations
degenerate elliptic fully nonlinear equations
2010/12/9
The solutions to the Dirichlet problem for two degenerate elliptic fully nonlinear equations in n + 1 dimensions, namely the real Monge-Amp`ere equation and the Donaldson equation, are shown to have m...