Nodal solutions of Yamabe-type equations on positive Ricci curvature manifolds

Abstract: We consider a closed cohomogeneity one Riemannian manifold $(M^n,g)$ of dimension $n\geq 3$. If the Ricci curvature of $M$ is positive, we prove the existence of infinite nodal solutions for equations of the form $-\Delta_g u + \lambda u = \lambda u<sup>q$ with $\lambda &gt;0$, $q&gt;1$. In particular for a positive Einstein manifold which is of cohomogeneity one or fibers over a cohomogeniety one Einstein manifold we prove the existence of infinite nodal solutions for the Yamabe equation, with a prescribed number of connected components of its nodal domain.