| Title:
|
Existence of solutions for nonlinear parabolic problems (English) |
| Author:
|
Halidias, Nikolaos |
| Author:
|
Papageorgiou, Nikolaos S. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
35 |
| Issue:
|
3 |
| Year:
|
1999 |
| Pages:
|
255-274 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider nonlinear parabolic boundary value problems. First we assume that the right hand side term is discontinuous and nonmonotone and in order to have an existence theory we pass to a multivalued version by filling in the gaps at the discontinuity points. Assuming the existence of an upper solution $\phi $ and of a lower solution $\psi $ such that $\psi \le \phi $, and using the theory of nonlinear operators of monotone type, we show that there exists a solution $x \in [\psi ,\phi ]$ and that the set of all such solutions is compact in $W_{pq}(T)$. For the problem with a Caratheodory right hand side we show the existence of extremal solutions in $[\psi ,\phi ]$. (English) |
| Keyword:
|
upper and lower solutions |
| Keyword:
|
weak solution |
| Keyword:
|
evolution triple |
| Keyword:
|
compact embedding |
| Keyword:
|
distributional derivative |
| Keyword:
|
operator of type $(S)_{+}$ |
| Keyword:
|
operator of type $L-(S)_{+}$ |
| Keyword:
|
$L$-pseudomonotone operator |
| Keyword:
|
multivalued problem |
| Keyword:
|
extremal solutions |
| Keyword:
|
Zorn’s lemma |
| MSC:
|
35K55 |
| MSC:
|
35K60 |
| idZBL:
|
Zbl 1046.35054 |
| idMR:
|
MR1725842 |
| . |
| Date available:
|
2008-06-06T22:23:23Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107700 |
| . |
| Reference:
|
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| . |
