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 |
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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 |
| _version_ | 1817997569590034432 |
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| author | D’Ambrosio Lorenzo Mitidieri Enzo |
| author_facet | D’Ambrosio Lorenzo Mitidieri Enzo |
| author_sort | D’Ambrosio Lorenzo |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-14T02:40:16Z |
| format | Article |
| id | doaj.art-9d20adff540546b1bcc95c21fc89b706 |
| institution | Directory Open Access Journal |
| issn | 2191-9496 2191-950X |
| language | English |
| last_indexed | 2024-04-14T02:40:16Z |
| publishDate | 2022-02-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advances in Nonlinear Analysis |
| spelling | doaj.art-9d20adff540546b1bcc95c21fc89b7062022-12-22T02:17:09ZengDe GruyterAdvances in Nonlinear Analysis2191-94962191-950X2022-02-0111178582910.1515/anona-2021-0217Entire solutions of certain fourth order elliptic problems and related inequalitiesD’Ambrosio Lorenzo0Mitidieri Enzo1Dipartimento di Matematica, Università degli Studi di Bari Aldo Moro, via E.Orabona, 4, I-70125BariDipartimento di Matematica e Geoscienze, Università degli Studi di Trieste, via A.Valerio, 12/1, I-34127TriesteWe 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.https://doi.org/10.1515/anona-2021-0217liouville theoremsbiharmonic operatorhardy–rellich inequalities35g2031b3035b5326d10 |
| spellingShingle | D’Ambrosio Lorenzo Mitidieri Enzo Entire solutions of certain fourth order elliptic problems and related inequalities Advances in Nonlinear Analysis liouville theorems biharmonic operator hardy–rellich inequalities 35g20 31b30 35b53 26d10 |
| title | Entire solutions of certain fourth order elliptic problems and related inequalities |
| title_full | Entire solutions of certain fourth order elliptic problems and related inequalities |
| title_fullStr | Entire solutions of certain fourth order elliptic problems and related inequalities |
| title_full_unstemmed | Entire solutions of certain fourth order elliptic problems and related inequalities |
| title_short | Entire solutions of certain fourth order elliptic problems and related inequalities |
| title_sort | entire solutions of certain fourth order elliptic problems and related inequalities |
| topic | liouville theorems biharmonic operator hardy–rellich inequalities 35g20 31b30 35b53 26d10 |
| url | https://doi.org/10.1515/anona-2021-0217 |
| work_keys_str_mv | AT dambrosiolorenzo entiresolutionsofcertainfourthorderellipticproblemsandrelatedinequalities AT mitidierienzo entiresolutionsofcertainfourthorderellipticproblemsandrelatedinequalities |