Entire solutions of certain fourth order elliptic problems and related inequalities
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2022-02-01
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| Series: | Advances in Nonlinear Analysis |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/anona-2021-0217 |
| Summary: | 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. |
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| ISSN: | 2191-9496 2191-950X |