Second eigenvalue of the Yamabe operator and applications

Let ((M,g)) be a compact Riemannian manifold of dimension (nge 3) . In this paper, we give various properties of the eigenvalues of the Yamabe operator (L_g) . In particular, we show how the second eigenvalue of (L_g) is related to the existence of nodal solutions of the equation (L_g u = {varepsilon }|u|^{N-2}u,) where ({varepsilon }= +1,) (0,) or (-1.)