A note on solutions of Yamabe-type equations on products of spheres

Abstract: We consider Yamabe-type equations on the Riemannian product of constant curvature metrics on $\textbf{S}ⁿ \times\textbf{ S}<sup>n$, and study solutions which are invariant by the cohomogeneity one diagonal action of $O(n+1)$. We obtain multiplicity results for both positive and nodal solutions. In particular we prove the existence of nodal solutions of the Yamabe equation on these products which depend non-trivially on both factors