Entire solutions of certain fourth order elliptic problems and related inequalities
| Autor: | D’Ambrosio Lorenzo, Mitidieri Enzo |
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| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Advances in Nonlinear Analysis, Vol 11, Iss 1, Pp 785-829 (2022) |
| Druh dokumentu: | article |
| ISSN: | 2191-9496 2191-950X |
| DOI: | 10.1515/anona-2021-0217 |
| Popis: | We study distributional solutions of semilinear biharmonic equations of the type Δ2u+f(u)=0 onℝN,{\Delta ^2}u + f(u) = 0\quad on\;{{\mathbb R} ^N}, where f is a continuous function satisfying f (t)t ≥ c |t|q+1 for all t ∈ ℝ with c > 0 and q > 1. By using a new approach mainly based on careful choice of suitable weighted test functions and a new version of Hardy- Rellich inequalities, we prove several Liouville theorems independently of the dimension N and on the sign of the solutions. |
| Databáze: | Directory of Open Access Journals |
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