| Title:
|
Nonlinear boundary value problems involving the extrinsic mean curvature operator (English) |
| Author:
|
Mawhin, Jean |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
139 |
| Issue:
|
2 |
| Year:
|
2014 |
| Pages:
|
299-313 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper surveys recent results obtained for the existence and multiplicity of radial solutions of Dirichlet problems of the type $$ \nabla \cdot \bigg (\frac {\nabla v}{\sqrt {1 - |\nabla v|^2}}\bigg ) = f(|x|,v) \quad \text {in} \ B_R,\quad u = 0 \quad \text {on} \ \partial B_R , $$ where $B_R$ is the open ball of center $0$ and radius $R$ in $\mathbb R^n$, and $f$ is continuous. Comparison is made with similar results for the Laplacian. Topological and variational methods are used and the case of positive solutions is emphasized. The paper ends with the case of a general domain. (English) |
| Keyword:
|
extrinsic mean curvature operator |
| Keyword:
|
Dirichlet problem |
| Keyword:
|
radial solution |
| Keyword:
|
positive solution |
| Keyword:
|
Leray-Schauder degree |
| Keyword:
|
critical point theory |
| MSC:
|
35-02 |
| MSC:
|
35A16 |
| MSC:
|
35B09 |
| MSC:
|
35B38 |
| MSC:
|
35J20 |
| MSC:
|
35J25 |
| MSC:
|
35J60 |
| MSC:
|
35J87 |
| MSC:
|
35J93 |
| idZBL:
|
Zbl 06362260 |
| idMR:
|
MR3238841 |
| DOI:
|
10.21136/MB.2014.143856 |
| . |
| Date available:
|
2014-07-14T08:34:16Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143856 |
| . |
| Reference:
|
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| . |
