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arXiv · 1301.0143

Multiplicity and asymptotic profile of 2-nodal solutions to a semilinear elliptic problem on a Riemannian manifold

Mónica Clapp·Anna Maria Micheletti
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Abstract

We establish a lower bound for the number of sign changing solutions with precisely two nodal domains to the singularly perturbed nonlinear elliptic equation -{\epsilon}^{2}{\Delta}_{g}u+u=|u|^{p-2}u on an n-dimensional Riemannian manifold M, p in (2,2n/(n-2)), in terms of the cup-length of the configuration space of M. We give a precise description of the asymptotic profile of these solutions as {\epsilon} goes to 0. We also provide new estimates for the cup-length of the configuration space of M.

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Mónica Clapp, Anna Maria Micheletti. 2013-01-01. Multiplicity and asymptotic profile of 2-nodal solutions to a semilinear elliptic problem on a Riemannian manifold. https://arxiv.org/abs/1301.0143

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