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 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.