Multiplicity of 2-nodal solutions of the Yamabe equation. (English) Zbl 07959975

Ortiz, Jorge Dávila; Barrantes González, Héctor; Munive Lima, Isidro H.

Topol. Methods Nonlinear Anal. 64, No. 1, 361-379 (2024).

Summary: Given a 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 non-linear equation on \((M,g)\), see (1.1) below. If \((N,h)\) is a closed Riemannian manifold of constant positive scalar curvature our result gives multiplicity results for the Yamabe-type equation on the Riemannian product \((M\times N, g + \varepsilon h)\), for \(\varepsilon > 0\) small.

MSC:

53C21	Methods of global Riemannian geometry, including PDE methods; curvature restrictions
58J05	Elliptic equations on manifolds, general theory

Keywords:

center of mass; gradient flow; nodal solution; Yamabe equation

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