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  • Existence results for some problems on Riemannian manifolds
    Molica Bisci, Giovanni, 1975- ; Repovš, Dušan, 1954- ; Vilasi, Luca
    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.
    Vir: Communications in analysis and geometry. - ISSN 1019-8385 (Vol. 28, no. 3, 2020, str. 677-706)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2020
    Jezik - angleški
    COBISS.SI-ID - 22044675

    Povezava(-e):

    https://dx.doi.org/10.4310/CAG.2020.v28.n3.a6
    Repozitorij Univerze v Ljubljani – RUL
    DOI

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