Existence results for some problems on Riemannian manifoldsMolica Bisci, Giovanni (Avtor) Repovš, Dušan (Avtor) Vilasi, Luca (Avtor) By using variational techniques we provide new existence results for Yamabe-type equations with subcritical perturbations set on a compact ▫$d$▫-dimensional (▫$d \ge 3$▫) Riemannian manifold without boundary. As a direct consequence of our main theorems, we prove the existence of at least one solution to the following Yamabe-type problem ▫$$\begin{cases} -\Delta_gw + \alpha(\sigma)w = \mu K(\sigma)w^{\frac{d+2}{d-2}} + \lambda (w^{r-1} + f(w)), \quad \sigma \in \mathcal{M} \\ w \in H^2_\alpha(\mathcal{M}), \quad w>0 \; \text{in} \; \mathcal{M}, \end{cases}$$▫ here, 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 furthermore solve some parametrized Emden-Fowler equations in the Euclidean case.20202020-08-17 07:55:12Članek v reviji118042sl