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

Marco Ghimenti | Zendy; Anna Maria Micheletti | Zendy

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

Author(s) -

Marco Ghimenti,

Anna Maria Micheletti

Publication year - 2012

Publication title -

communications on pure andamp applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.077

H-Index - 42

eISSN - 1553-5258

pISSN - 1534-0392

DOI - 10.3934/cpaa.2013.12.679

Subject(s) - degenerate energy levels , degeneracy (biology) , mathematics , sign (mathematics) , manifold (fluid mechanics) , riemannian manifold , nonlinear system , metric (unit) , mathematical analysis , pure mathematics , upper and lower bounds , physics , quantum mechanics , mechanical engineering , bioinformatics , operations management , engineering , economics , biology

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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