  We consider Yamabe-type equations on Projective Spaces
  $\mathbb{C} {\bf P}^n$ and $\mathbb{H} {\bf P}^n$ with the respectives
canonical metrics, and study the existence and multiplicity of solutions of
Yamabe-type equation, which are invariant by cohomogeneity one actions of $
U(n)$ and $Sp(n)$ respectively. We also prove the existence of degenerate
solutions of the Yamabe-type equationn on $\mathbb{C} {\bf P}^n$ and
$\mathbb{H} {\bf P}^n$, which are invariant by cohomogeneity one actions of $
U(n)$ and $Sp(n)$ respectively.
