| Title:
|
On the existence of free vibrations for a beam equation when the period is an irrational multiple of the length (English) |
| Author:
|
Feireisl, Eduard |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
33 |
| Issue:
|
2 |
| Year:
|
1988 |
| Pages:
|
94-102 |
| Summary lang:
|
English |
| Summary lang:
|
Russian |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
The author examined non-zero $T$-periodic (in time) solutions for a semilinear beam equation under the condition that the period $T$ is an irrational multiple of the length. It is shown that for a.e. $T \in R^1$ (in the sense of the Lebesgue measure on $R^1$) the solutions do exist provided the right-hand side of the equation is sublinear. (English) |
| Keyword:
|
nonuniqueness |
| Keyword:
|
time-periodical solutions |
| Keyword:
|
semilinear equation |
| Keyword:
|
irrational periods |
| Keyword:
|
dual variational method |
| MSC:
|
35B10 |
| MSC:
|
35K60 |
| MSC:
|
35L70 |
| MSC:
|
58E05 |
| MSC:
|
73K12 |
| idZBL:
|
Zbl 0684.35057 |
| idMR:
|
MR0940709 |
| DOI:
|
10.21136/AM.1988.104291 |
| . |
| Date available:
|
2008-05-20T18:34:06Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104291 |
| . |
| Reference:
|
[1] J. M. Coron: Periodic solutions of a nonlinear wave equation without assumption of monotonicity.Math. Ann. 262 (1983), 273-285. Zbl 0489.35061, MR 0690201, 10.1007/BF01455317 |
| Reference:
|
[2] D. G. Costa M. Willem: Multiple critical points of invariant functional and applications.Séminaire de Mathématique 2-éme Semestre Université Catholique de Louvain. |
| Reference:
|
[3] I. Ekeland R. Temam: Convex analysis and variational problems.North-Holland Publishing Company 1976. MR 0463994 |
| Reference:
|
[4] N. Krylová O. Vejvoda: A linear and weakly nonlinear equation of a beam: the boundary value problem for free extremities and its periodic solutions.Czechoslovak Math. J. 21 (1971), 535-566. MR 0289918 |
| . |
