NODAL SOLUTIONS OF YAMABE-TYPE EQUATIONS ON POSITIVE RICCI CURVATURE MANIFOLDS

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 -Delta(g)u + lambda u = lambda u(q) with lambda > 0, q > 1. In particular for a positive Einstein manifold which is of cohomogeneity one or fibers over a cohomogeneity 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.

Automated summary

For a closed cohomogeneity one Riemannian manifold of dimension n ≥ 3 with positive Ricci curvature, infinite nodal solutions for certain equations can be proven to exist. Specifically, for a positive Einstein manifold of cohomogeneity one or fibered over such a manifold, the existence of infinite nodal solutions for the Yamabe equation can be established with a prescribed number of connected components of its nodal domain.