Giovanni Molica Bisci (Avtor), Dušan Repovš (Avtor), Luca Vilasi (Avtor)

Povzetek

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.

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Podatki

Jezik: Angleški jezik
Leto izida:
Tipologija: 1.01 - Izvirni znanstveni članek
Organizacija: UL FMF - Fakulteta za matematiko in fiziko
UDK: 517.956
COBISS: 22044675 Povezava se bo odprla v novem oknu
ISSN: 1019-8385
Št. ogledov: 371
Št. prenosov: 166
Ocena: 0 (0 glasov)
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Ostali podatki

Vrsta dela (COBISS): Članek v reviji
Strani: str. 677-706
Letnik: ǂVol. ǂ28
Zvezek: ǂno. ǂ3
Čas izdaje: 2020
DOI: 10.4310/CAG.2020.v28.n3.a6
ID: 11959893