Some results about semilinear elliptic problems on half-spaces
We prove some new results about the growth, the monotonicity and the symmetry of (possibly) unbounded non-negative solutions of −∆u = f (u) on half-spaces, where f is merely a locally Lipschitz continuous function. Our proofs are based on a comparison principle for solutions of semilinear problems o...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2020-10-01
|
| Series: | Mathematics in Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/10.3934/mine.2020033/fulltext.html |
| id |
doaj-1b7f5724d20f4292a43fbf398f5949c4 |
|---|---|
| record_format |
Article |
| spelling |
doaj-1b7f5724d20f4292a43fbf398f5949c42020-11-25T03:46:44ZengAIMS PressMathematics in Engineering2640-35012020-10-012470972110.3934/mine.2020033Some results about semilinear elliptic problems on half-spacesAlberto Farina0LAMFA, CNRS UMR 7352, Université de Picardie Jules Verne, 33 rue Saint-Leu, 80039 Amiens, FranceWe prove some new results about the growth, the monotonicity and the symmetry of (possibly) unbounded non-negative solutions of −∆u = f (u) on half-spaces, where f is merely a locally Lipschitz continuous function. Our proofs are based on a comparison principle for solutions of semilinear problems on unbounded slab-type domains and on the moving planes method.https://www.aimspress.com/article/10.3934/mine.2020033/fulltext.htmlqualitative properties of solutions to semilinear elliptic equationsmoving planes methodcomparison principle |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Alberto Farina |
| spellingShingle |
Alberto Farina Some results about semilinear elliptic problems on half-spaces Mathematics in Engineering qualitative properties of solutions to semilinear elliptic equations moving planes method comparison principle |
| author_facet |
Alberto Farina |
| author_sort |
Alberto Farina |
| title |
Some results about semilinear elliptic problems on half-spaces |
| title_short |
Some results about semilinear elliptic problems on half-spaces |
| title_full |
Some results about semilinear elliptic problems on half-spaces |
| title_fullStr |
Some results about semilinear elliptic problems on half-spaces |
| title_full_unstemmed |
Some results about semilinear elliptic problems on half-spaces |
| title_sort |
some results about semilinear elliptic problems on half-spaces |
| publisher |
AIMS Press |
| series |
Mathematics in Engineering |
| issn |
2640-3501 |
| publishDate |
2020-10-01 |
| description |
We prove some new results about the growth, the monotonicity and the symmetry of (possibly) unbounded non-negative solutions of −∆u = f (u) on half-spaces, where f is merely a locally Lipschitz continuous function. Our proofs are based on a comparison principle for solutions of semilinear problems on unbounded slab-type domains and on the moving planes method. |
| topic |
qualitative properties of solutions to semilinear elliptic equations moving planes method comparison principle |
| url |
https://www.aimspress.com/article/10.3934/mine.2020033/fulltext.html |
| work_keys_str_mv |
AT albertofarina someresultsaboutsemilinearellipticproblemsonhalfspaces |
| _version_ |
1724504592898588672 |