  We study the problem of deforming a Riemannian metric to a conformal one with
nonzero constant scalar curvature and nonzero constant boundary mean curvature
on a compact manifold of dimension $n\geq 3$. We prove the existence of such
conformal metrics in the cases of $n=6,7$ or the manifold is spin and some
other remaining ones left by Escobar. Furthermore, in the positive Yamabe
constant case, by normalizing the scalar curvature to be $1$, there exists a
sequence of conformal metrics such that their constant boundary mean curvatures
go to $+\infty$.
