| Title:
|
On periodic solution of a nonlinear beam equation (English) |
| Author:
|
Kopáčková, Marie |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
28 |
| Issue:
|
2 |
| Year:
|
1983 |
| Pages:
|
108-115 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
the existence of an $\omega$-periodic solution of the equation $\frac {\partial^2u}{\partial t^2} + \alpha \frac {\partial^4u} {\partial x^4} + \gamma \frac {\partial^5u}{\partial x^4\partial t} - \tilde{\gamma} \frac {\partial^3u}{\partial x^2\partial t} + \delta \frac {\partial u}{\partial t} - \left[\beta + \aleph\int^n_0{\left(\frac {\partial u}{\partial x}\right)}^2 (\cdot,\xi)d\xi + \sigma \int^n_0 \frac {\partial^2u}{\partial x \partial t} (\cdot,\xi) \frac {\partial u}{\partial x}(\cdot,\xi)d \xi \right] \frac {\partial^2u}{\partial x^2}=f$ sarisfying the boundary conditions $u(t,0)=u(t,\pi)=\frac{\partial^2u}{\partial x^2}\left(t,0\right)=\frac{\partial^2u}{\partial x^2}\left(t,\pi\right)=0$ is proved for every $\omega$-periodic function $f\in C\left(\left[0,\omega\right],L_2\right)$. (English) |
| Keyword:
|
periodic solution |
| Keyword:
|
nonlinear beam equation |
| Keyword:
|
existence |
| MSC:
|
35B10 |
| MSC:
|
35G30 |
| MSC:
|
45K05 |
| MSC:
|
47A10 |
| MSC:
|
73K12 |
| MSC:
|
74K10 |
| idZBL:
|
Zbl 0533.35003 |
| idMR:
|
MR0695184 |
| DOI:
|
10.21136/AM.1983.104011 |
| . |
| Date available:
|
2008-05-20T18:21:27Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104011 |
| . |
| Reference:
|
[1] V. B. Litvinov, Ju. V. Jadykin: Vibration of Extensible Thin Bodies in Transversal Flow.Dokl. Akad. Nauk Ukrain. SSR, Ser. A, No 4 (1981) 47-50. |
| Reference:
|
[2] J. M. Ball: Stability Theory for an Extensible Beam.J. Differential Equations 14 (1973), 399-418. Zbl 0247.73054, MR 0331921, 10.1016/0022-0396(73)90056-9 |
| Reference:
|
[3] T. Narazaki: On the Time Global Solutions of Perturbed Beam Equations.Proc. Fac. Sci. Tokai Univ. 16 (1981), 51-71. Zbl 0474.35010, MR 0632661 |
| Reference:
|
[4] V. Lovicar: Periodic Solutions of Nonlinear Abstract Second Order Equations with Dissipative Terms.Čas. Pěst. Mat. 102 (1977), 364-369. Zbl 0369.34017, MR 0508656 |
| Reference:
|
[5] N. Dunford J. T. Schwartz: Linear operators I.(Intersci. Publ. New York-London) 1958. MR 0117523 |
| . |
