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

2013/01/01 by Mónica Clapp, Clapp, Mónica, Anna Maria Micheletti +1 · 1 citation
Computer Science · Mathematics · #35J61 #35R01 #55R12 #55R80 (Secondary) #58J05 (Primary) 35B25 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1301.0143

openalex publication_date 2013/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 -ε²Δ_gu+u=|u|^p-2u 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 ε goes to 0. We also provide new estimates for the cup-length of the configuration space of M.

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