Solutions of the Yamabe Equation By Lyapunov-Schmidt Reduction

Given any closed Riemannian manifold $(M,g)$ we use the Lyapunov-Schmidt finite-dimensional reduction method to prove multiplicity results for positive 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 Yamabe equation on the Riemannian product $(M\times N, g + \epsilon^{2} h)$, for $\epsilon >0$ small.