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 ≥ 3. If the Ricci curvature of M is positive, we prove the existence of infinite nodal solutions for equations of the form −∆ g u + λu = λu q with λ > 0, q > 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.