Bifurcation of metrics with null scalar curvature and constant mean curvature on the boundary of compact manifolds

In the present paper we study multiplicity results for a Yamabe-type problem proposed by Escobar in 1992. We consider the product of a compact Riemannian manifold without boundary and null scalar curvature with a compact Riemannian manifold with boundary, having null scalar curvature and constant mean curvature on the boundary. We use some standard results from the bifurcation theory to prove the existence of an infinite number of conformal classes with at least two non-homothetic Riemannian metrics of null scalar curvature and constant mean curvature on the boundary of the product manifold. In addition, we obtain a convergence result for bifurcating branches.