| Title:
|
An existence theorem for the v. Kármán equations under the condition of free boundary (English) |
| Author:
|
Naumann, Joachim |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
19 |
| Issue:
|
1 |
| Year:
|
1974 |
| Pages:
|
17-27 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper concerns the v. Kármán equations governing the bending of a thin elastic plate under the condition of free boundary. Starting from the definition of a variational solution, the boundary value problem considered is replaced by an equivalent abstract operator equation to which the known theorems of the nonlinear operator theory apply. The main result consists in an existence theorem of a variational solution for the problem under consideration. () |
| MSC:
|
35B45 |
| MSC:
|
35D05 |
| MSC:
|
35G20 |
| MSC:
|
35Q99 |
| idZBL:
|
Zbl 0291.35011 |
| idMR:
|
MR0346294 |
| DOI:
|
10.21136/AM.1974.103510 |
| . |
| Date available:
|
2008-05-20T17:58:00Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103510 |
| . |
| Reference:
|
[1] Berger M. S., Fife P.: On von Karman's equations and the buckling of a thin elastic plate.11. Plate with general edge conditions. - Comm. Pure Appl. Math.,21 (1968), 227- 241. MR 0229978, 10.1002/cpa.3160210303 |
| Reference:
|
[2] Fife P.: Non-linear deflection of thin elastic plates under tension.- Comm. Pure Appl. Math., 14 (1961), 81 - 112. Zbl 0099.40802, MR 0128697, 10.1002/cpa.3160140202 |
| Reference:
|
[3] Knightly G. H.: An existence theorem for the von Kármán equations.- Arch. Rat. Mech. Anal., 27 (1967), 233 - 242. Zbl 0162.56303, MR 0220472, 10.1007/BF00290614 |
| Reference:
|
[4] Knightly G. H., Sather D.: On nonuniqueness of solutions of the von Kármán equations.- Arch. Rat. Mech. Anal., 36 (1970), 65-78. Zbl 0188.57603, MR 0261835, 10.1007/BF00255747 |
| Reference:
|
[5] Morozov N. F.: Nonlinear problems in the theory of thin plates.(Russian). - Vestnik Leningr. Univ., 19 (1958), 100-124. MR 0102224 |
| Reference:
|
[6] Nečas J.: Les méthodes directes en théorie des équations elliptiques.- Academia, Prague 1967. MR 0227584 |
| Reference:
|
[7] Sharij Ju. I., Jurchenko A. S.: Dirichleťs problem for equations of Karman's type.- Diff. urav., 4(1968), 1713-1719. MR 0235279 |
| . |
