| Title:
|
Periodic solutions of a weakly nonlinear hyperbolic equation in $E_2$ and $E_3$ (English) |
| Author:
|
Vítek, Václav |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
19 |
| Issue:
|
4 |
| Year:
|
1974 |
| Pages:
|
232-245 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
For $n=2$ and 3 the existence and uniqueness of classical periodic solution of $\square_nu+2au_t+2(B,\nabla_nu)+cu=h(t,x)+\epsilon f(t,x,u,\epsilon)$ $(x=(x_1, x_2,\ldots,x_n))$ is proved assuming the periodicity of the right-hand side. () |
| MSC:
|
35B10 |
| MSC:
|
35B20 |
| MSC:
|
35L60 |
| idZBL:
|
Zbl 0311.35004 |
| idMR:
|
MR0402292 |
| DOI:
|
10.21136/AM.1974.103537 |
| . |
| Date available:
|
2008-05-20T17:59:12Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103537 |
| . |
| Reference:
|
[1] R. Courant D. Hilbert: Methoden der mathematischen Physik.Vol. 2, Berlin 1937. |
| Reference:
|
[2] F. A. Ficken B. A. Fleishman: Initial value problems and time-periodic solutions for a nonlinear wave equation.Comm. pure appl. math. 10 (1957), 331 - 356. MR 0092080, 10.1002/cpa.3160100303 |
| Reference:
|
[3] J. Havlová: Periodic solutions of a nonlinear telegraph equation.Čas. pěst. mat. 90 (1965), 273-289. MR 0192180 |
| Reference:
|
[4] L. V. Kantorovič G. P. Akilov: Funkcionaľnyj analiz v normirovanych prostranstvach.Moskva 1959. |
| Reference:
|
[5] G. N. Watson: A treatise on the theory of Bessel functions.2nd ed. Cambridge U.P. 1944. Zbl 0063.08184, MR 0010746 |
| . |
