Multiplicity of 2-nodal solutions of the Yamabe equation - Ortiz, Jorge Dávila; González, Héctor Barrantes; Lima, Isidro H. Munive (Topological Methods in Nonlinear Analysis, 2024)
Given a closed Riemannian manifold (M,g), we use the gradient flow method and Sign-Changing Critical Point Theory to prove multiplicity results for 2-nodal solutions of a subcritical non-linear equation on (M,g), see yam-nodal-1 below. If (N,h) is a closed Riemannian manifold of constant positive scalar curvature our result gives multiplicity results for the Yamabe-type equation on the Riemannian product (M× N , g + h ), for > 0 small.