| Title:
|
Periodic solutions to weakly nonlinear autonomous wave equations (English) |
| Author:
|
Štědrý, Milan |
| Author:
|
Vejvoda, Otto |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
25 |
| Issue:
|
4 |
| Year:
|
1975 |
| Pages:
|
536-555 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| MSC:
|
35B10 |
| MSC:
|
35L05 |
| idZBL:
|
Zbl 0319.35052 |
| idMR:
|
MR0393762 |
| DOI:
|
10.21136/CMJ.1975.101350 |
| . |
| Date available:
|
2008-06-09T14:14:49Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/101350 |
| . |
| Reference:
|
[1] M. S. Berger: On periodic solutions of nonlinear hyperbolic equations and the calculus of variations.Bull. Amer. Math. Soc, 76 (1970), 633-637. Zbl 0209.40701, MR 0254406, 10.1090/S0002-9904-1970-12467-3 |
| Reference:
|
[2] M. S. Berger: Stationary states for a nonlinear wave equation.J. Math. Physics, 11 (1970), 2906--2912. Zbl 0201.12602, MR 0274969, 10.1063/1.1665460 |
| Reference:
|
[3] M. S. Berger: On the existence and structure of stationary states for a nonlinear Klein-Gordan equation.J. Functional Analysis, 9 (1972), 249-261. MR 0299966, 10.1016/0022-1236(72)90001-8 |
| Reference:
|
[4] J. P. Fink W. S. Hall: Entrainment of frequency in evolution equation.J. Diff. Eq. 14 (1973), 9-41 MR 0346261, 10.1016/0022-0396(73)90074-0 |
| Reference:
|
[5] J. P. Fink W. S. Hall S. Khalili: Perturbation expansions for some nonlinear wave equations.SIAM J. Appl. Math. 24 (1973), 575-595. MR 0315256, 10.1137/0124060 |
| Reference:
|
[6] B. A. Fleishman: Progressing waves in an infinite nonlinear string.Proc. Amer. Math. Soc. 10 (1959), 329-334. MR 0105903, 10.1090/S0002-9939-1959-0105903-X |
| Reference:
|
[7] J. B. Keller L. Ting: Periodic vibrations of systems governed by nonlinear partial differential equations.Comm. Pure Appl. Math. 19 (1966), 371-420. MR 0205520, 10.1002/cpa.3160190404 |
| Reference:
|
[8] J. Kurzweil: Exponentially stable integral manifolds, averaging principle and continuous dependence on a parameter.Czech. Math. J. 16 (91) (1966), 380-423, 463-491. Zbl 0186.47701, MR 0206440 |
| Reference:
|
[9] J. Kurzweil: Van der Pol perturbation of the equation for a vibrating string.Czech. Math. J. 77 (92), (1967), 558-608. Zbl 0164.41003, MR 0219863 |
| Reference:
|
[10] M. H. Millman J. B. Keller: Perturbation theory of nonlinear boundary-value problems.J. Math. Physics, 10 (1969), 342-361. MR 0237867, 10.1063/1.1664849 |
| Reference:
|
[11] K. Petiau: Sur une généralisation non linéaire de la mécanique ondulatoire et les propriétés des fonctions d'ondes correspondantes.Nuovo Cimento, 9 (1958), 542-568. Zbl 0082.22403, MR 0103063, 10.1007/BF02747687 |
| Reference:
|
[12] S. I. Pochozajev: On periodic solutions of some nonlinear hyperbolic equations.(Russian), Dokl. AN SSSR, 198 (1971), 1274-1277. MR 0284688 |
| Reference:
|
[13] O. Vejvoda: Periodic solutions of a linear and weakly nonlinear wave equation in one dimension I.Czech. Math. J. 14 (1964), 341-382. MR 0174872 |
| Reference:
|
[14] O. Vejvoda: The mixed problem and periodic solutions for a linear and weakly nonlinear wave equation in one dimension.Rozpravy ČSAV, řada mat. a přir. věd, 80 (1970), 5, Academia, Praha. Zbl 0278.35064, MR 0310437 |
| Reference:
|
[15] V. A. Vitt: Self-excited transmission lines.(Russian), Žurn. Teoret. Fiz., 4 (1934), 144-157. |
| Reference:
|
[16] M. E, Žabotinskij: On periodic solutions of nonlinear partial differential equations.Dokl. AN SSSR, 56 (1947), 469-472. MR 0022015 |
| . |
