Sign-changing blow-up for the Yamabe equation at the lowest energy level (Q2099104)

The paper studies the blow-up behavior of sequences of nodal solutions to the Yamabe equation on a Riemannian manifold of positive Yamabe type. Whenever the dimension is between 11 and 24, the authors show that the set of sign-changing solutions is not compact. This contrasts to the case of the set of positive solutions, which is known to be compact. The paper also contains existence and compactness results. The proofs rely on a Lyapunov-Schmidt reduction method, where a nodal blowing-up sequence of approximate solutions is constructed as a saddle-type critical point of a reduced energy. The profiles are of the form \(-u_0+B_k+\)lower order terms, where \(u_0>0\) is a positive solution and \(B_k\) is a positive bubbling profile.