Multiplicity of 2-nodal solutions the Yamabe equation

Given any closed Riemannian manifold \((M, g)\), we use the gradient flow method and Sign-Changing Critical Point Theory to prove multiplicity results for 2-nodal solutions of a subcritical Yamabe type equation on \((M, g)\). If \((N, h)\) is a closed Riemannian manifold of constant positive scalar...

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Bibliographic Details
Published inarXiv.org
Main Authors DÁvila, Jorge, Héctor Barrantes G, Munive, Isidro H
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 13.06.2023
Subjects
Critical point
Gradient flow
Riemann manifold
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Summary:Given any closed Riemannian manifold \((M, g)\), we use the gradient flow method and Sign-Changing Critical Point Theory to prove multiplicity results for 2-nodal solutions of a subcritical Yamabe type equation on \((M, g)\). If \((N, h)\) is a closed Riemannian manifold of constant positive scalar curvature our result gives multiplicity results for the type Yamabe equation on the Riemannian product \((M x N, g + \epsilon h)\), for \(\epsilon > 0\) small.
ISSN:2331-8422