  By using variational techniques we provide new existence results for
Yamabe-type equations with subcritical perturbations set on a compact
$d$-dimensional ($d\geq 3$) Riemannian manifold without boundary. As a direct
consequence of our main theorems, we prove the existence of at least one
solution to the following singular Yamabe-type problem $$ \left\lbrace
\begin{array}{ll} -\Delta_g w + \alpha(\sigma)w = \mu K(\sigma)
w^\frac{d+2}{d-2} +\lambda \left( w^{r-1} + f(w)\right), \quad
\sigma\in\mathcal{M} &\\ &\\ w\in H^2_\alpha(\mathcal{M}), \quad w>0 \ \
\mbox{in} \ \ \mathcal{M} & \end{array} \right.$$ where, as usual, $\Delta_g$
denotes the Laplace-Beltrami operator on $(\mathcal{M},g)$, $\alpha,
K:\mathcal{M}\to\mathbb{R}$ are positive (essentially) bounded functions,
$r\in(0,1)$, and $f:[0,+\infty)\to[0,+\infty)$ is a subcritical continuous
function. Restricting ourselves to the unit sphere ${\mathbb{S}}^d$ via the
stereographic projection, we also solve some parametrized Emden-Fowler
equations in the Euclidean case.
