Szczegóły publikacji
Opis bibliograficzny
Positive supersolutions of fourth-order nonlinear elliptic equations: explicit estimates and Liouville theorems / Asadollah Aghajani, Craig Cowan, Vicenţiu D. RĂDULESCU // Journal of Differential Equations ; ISSN 0022-0396. — 2021 — vol. 298, s. 323–345. — Bibliogr. s. 344–345, Abstr. — Publikacja dostępna online od: 2021-07-15. — V. D. Rădulescu - dod. afiliacje: University of Craiova, Craiova, Romania; ’Simion Stoilow’ Institute of Mathematics of the Romanian Academy, Bucharest, Romania
Autorzy (3)
- Aghajani Asadollah
- Cowan Craig
- AGHRǎdulescu Vicenţiu
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 135532 |
|---|---|
| Data dodania do BaDAP | 2021-08-31 |
| Tekst źródłowy | URL |
| DOI | 10.1016/j.jde.2021.07.005 |
| Rok publikacji | 2021 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Czasopismo/seria | Journal of Differential Equations |
Abstract
In this paper, we consider positive supersolutions of the semilinear fourth-order problem {(−Δ)2u=ρ(x)f(u)inΩ,−Δu>0inΩ, where Ω is a domain in RN (bounded or not), f:Df=[0,af)→[0,∞) (0f⩽+∞) is a non-decreasing continuous function with f(u)>0 for u>0 and ρ:Ω→R is a positive function. Using a maximum principle-based argument, we give explicit estimates on positive supersolutions that can easily be applied to obtain Liouville-type results for positive supersolutions either in exterior domains, or in unbounded domains Ω with the property that supx∈Ωdist(x,∂Ω)=∞. In particular, we consider the above problem with f(u)=up (p>0) and with different weights ρ(x)=|x|a, eax or x1m (m is an even integer). Also, when f is convex and ρ:Ω→(0,∞) is smooth with Δ(ρ)>0, then under an extra condition between f and ρ we show that every positive supersolution u of this problem with u=0 on ∂Ω (Ω bounded) satisfies the inequality −Δu≥2ρ(x)F(u) for all x∈Ω, where F(t):=∫0t(f(s)−f(0))ds.
