Abstract
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.
Keywords
No keyword data available
Data
Language: |
English |
Year of publishing: |
2020 |
Typology: |
1.01 - Original Scientific Article |
Organization: |
UL FMF - Faculty of Mathematics and Physics |
UDC: |
517.956 |
COBISS: |
22044675
|
ISSN: |
1019-8385 |
Views: |
371 |
Downloads: |
166 |
Average score: |
0 (0 votes) |
Metadata: |
|
Other data
Type (COBISS): |
Article |
Pages: |
str. 677-706 |
Volume: |
ǂVol. ǂ28 |
Issue: |
ǂno. ǂ3 |
Chronology: |
2020 |
DOI: |
10.4310/CAG.2020.v28.n3.a6 |
ID: |
11959893 |