2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/155510Let $(M,g)$ be a compact Riemannian manifold of dimension $n \geq 3$. We define the second Yamabe invariant as the infimum of the second eigenvalue of the Yamabe operator over the metrics conformal to $g$ and of volume 1. We study when it is attained. As an application, we find nodal solutions of the Yamabe equation.Differential Geometry53A30, 35J60 (Primary) 35P30, 58J50, 58C40 (Secondary)text