20.500.12556/RUL-118042 Existence results for some problems on Riemannian manifolds 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. true false true Angleški jezik Ni določen Članek v reviji 2020-08-17 07:55:12 2020-08-17 07:55:16 2022-08-30 04:01:12 0000-00-00 00:00:00 2020 0 0 Str. 677-706 no. 3 Vol. 28 2020 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 517.956 1019-8385 10.4310/CAG.2020.v28.n3.a6 22044675 3760729 RAZ_Molica_Bisci_Giovanni_2020.pdf RAZ_Molica_Bisci_Giovanni_2020.pdf 1 A065995035B257300C66B7B468561683 4caa40bd2d9d16d1e4e7a379081bce32a39cc102ced84d626eb207e2f0fc2085 4d5dcc9a-a1b9-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=131976 Pedagoška fakulteta Fakulteta za matematiko in fiziko 0 0 0