| Title:
|
Free vibrations for the equation of a rectangular thin plate (English) |
| Author:
|
Feireisl, Eduard |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
33 |
| Issue:
|
2 |
| Year:
|
1988 |
| Pages:
|
81-93 |
| Summary lang:
|
English |
| Summary lang:
|
Russian |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the paper, we deal with the equation of a rectangular thin plate with a simply supported boundary. The restoring force being an odd superlinear function of the vertical displacement, the existence of infinitely many nonzero time-periodic solutions is proved. (English) |
| Keyword:
|
thin plate |
| Keyword:
|
simply supported |
| Keyword:
|
existence |
| Keyword:
|
infinitely many nonzero time-periodic solutions |
| Keyword:
|
Ljusternik-Schnirelman theory |
| Keyword:
|
approximate solution |
| MSC:
|
35B10 |
| MSC:
|
35L70 |
| MSC:
|
58E05 |
| MSC:
|
73K12 |
| MSC:
|
74H45 |
| MSC:
|
74K20 |
| idZBL:
|
Zbl 0648.73024 |
| idMR:
|
MR0940708 |
| DOI:
|
10.21136/AM.1988.104290 |
| . |
| Date available:
|
2008-05-20T18:34:03Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104290 |
| . |
| Reference:
|
[1] H. Amann G. Mancini: Some applications of monotone operator theory to resonance problems.Nonlinear Anal. 3 (1979), 815-830. MR 0548954, 10.1016/0362-546X(79)90050-6 |
| Reference:
|
[2] K. C. Chang L. Sanchez: Nontrivial periodic solutions of a nonlinear beam equation.Math. Meth. in the Appl. Sci. 4 (1982), 194-205. MR 0659037, 10.1002/mma.1670040113 |
| Reference:
|
[3] E. Feireisl: On periodic solutions of a beam equation.(Czech.). Thesis, Fac. Math. Phys. of Charles Univ., Prague 1982. |
| Reference:
|
[4] V. Lovicar: Free vibrations for the equation $u_{tt} - u_{xx} + f(u) = 0$ with f sublinear.Proceedings of EQUADIFF 5, Teubner Texte zur Mathematik, Band 47, 228-230. MR 0715981 |
| Reference:
|
[5] P. H. Rabinowitz: Free vibrations for a semilinear wave equation.Comm. Pure Appl. Math. 31 (1978), 31-68. Zbl 0341.35051, MR 0470378, 10.1002/cpa.3160310103 |
| . |
