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Periodic vibrations of systems governed by nonlinear partial differential equations

1966; Wiley; Volume: 19; Issue: 4 Linguagem: Inglês

10.1002/cpa.3160190404

1097-0312

Joseph B. Keller, Lu Ting,

Differential Equations and Numerical Methods

Communications on Pure and Applied MathematicsVolume 19, Issue 4 p. 371-420 Article Periodic vibrations of systems governed by nonlinear partial differential equations Joseph B. Keller, Joseph B. KellerSearch for more papers by this authorLu Ting, Lu TingSearch for more papers by this author Joseph B. Keller, Joseph B. KellerSearch for more papers by this authorLu Ting, Lu TingSearch for more papers by this author First published: November 1966 https://doi.org/10.1002/cpa.3160190404Citations: 104AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Bibliography 1 Carrier, G., On the non-linear vibration problem of the elastic string, Quart. Appl. Math., Vol. 3, 1945, pp. 157– 165. A note on the vibrating string, Quart. Appl. Math., Vol. 7, 1949, pp. 97– 101. 2 Stoker, J. J., Periodic motions in non-linear systems having infinitely many degrees of freedom, Actes du Colloque International des Vibrations Non Lineaires, Publications Scientifiques et Techniques du Ministères de L'air, No. 281, Paris, 1953, pp. 61– 74. 3 Tadjbakhsh, I., and Keller, J. B., Standing surface waves of finite amplitude, J. Fluid Mech., Vol. 8, 1960, pp. 442– 451. 4 Verma, G. R., and Keller, J. B., Three-dimensional standing surface waves of finite amplitude, Physics of Fluids, Vol. 5, 1962, pp. 52– 56. 5 Concus, P., Standing capillary-gravity waves of finite amplitude, J. Fluid Mech., Vol. 14, 1962, pp. 568– 576. 6 Lax, P. D., Development of singularities of solutions of nonlinear hyperbolic partial differential equations, J. Math. Phys., Vol. 5, 1964, pp. 611– 613. 7 Cesari, L., Periodic solutions of hyperbolic partial differential equations, International Symposium on Nonlinear Differential Equations and Nonlinear Mechanics, Academic Press, New York, 1963, pp. 33– 57. 8 Rabinowitz, P. H., Periodic solutions of a nonlinear non-dissipative wave equation, New York University, Courant Inst. Math. Sci., Res. Report No. IMM 343, 1965. Citing Literature Volume19, Issue4November 1966Pages 371-420 ReferencesRelatedInformation