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Let be a compact Riemannian manifold of dimension .We suppose that is a metric in the Sobolev space with and there exist a point and such that is smooth in the ball . We define the second Yamabe invariant with singularities as the infimum of the second eigenvalue of the singular Yamabe operator over a generalized class of conformal metrics to and of volume . We show that this operator is attained by a generalized metric, we deduce nodal solutions to a Yamabe type equation with...
Subalgebras of germs of vector fields leaving fixed in , of finite codimension in symplectic Lie algebra contain the ideal of germs infinitely flat at . We give an application.
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