Non degeneracy for solutions of singularly perturbed nonlinear elliptic problems on symmetric Riemannian manifolds

Details Non degeneracy for solutions of singularly perturbed nonlinear elliptic problems on symmetric Riemannian manifolds Non degeneracy for solutions of singularly perturbed nonlinear elliptic problems on symmetric Riemannian manifolds

2011-06-02

arxiv.org/abs/1106.0460v1

Mathematics

Analysis of PDEs

Scientific paper

Given a symmetric Riemannian manifold (M, g), we show some results of
genericity for non degenerate sign changing solutions of singularly perturbed
nonlinear elliptic problems with respect to the parameters: the positive number
{\epsilon} and the symmetric metric g. Using these results we obtain a lower
bound on the number of non degenerate solutions which change sign exactly once.

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