Non degeneracy for solutions of singularly perturbed nonlinear elliptic problems
on symmetric Riemannian manifolds
Marco Ghimenti - Dipartimento di Matematica Applicata, Università di Pisa, via Buonarroti 1c, 56127, Pisa, Italy (email)
Abstract: 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 $\varepsilon$ 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.
Keywords: Symmetric Riemannian manifolds, non degenerate
sign changing solutions, singularly perturbed nonlinear elliptic problems.
Received: June 2011; Revised: December 2011; Published: September 2012.
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