  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.
