Multiplicity of 2-nodal solutions the Yamabe equation

Abstract

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 $(MxN,g+\epsilon h)$, for $\epsilon >0$ small.