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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
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Category: math
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MSC: 35B10
MSC: 35L05
idZBL: Zbl 0319.35052
idMR: MR0393762
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Date available: 2008-06-09T14:14:49Z
Last updated: 2016-04-06
Stable URL: http://hdl.handle.net/10338.dmlcz/101350
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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
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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
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