  Let $(M,g)$ be a compact Riemannian manifold with non-empty boundary.
Provided $f$ an isoparametric function of $(M,g)$ we prove existence results
for positive solutions of the Yamabe equation that are constant along the level
sets of $f$. If $(M,g)$ has positive constant scalar curvature, minimal
boundary and admits an isoparametric function we also prove multiplicity
results for positive solutions of the Yamabe equation on $(M \times N,g+th) $
where $(N,h)$ is any closed Riemannian manifold with positive constant scalar
curvature.
