×

zbMATH — the first resource for mathematics

Periodic solutions of a class of weakly nonlinear evolution equations. (English) Zbl 0211.12704

MSC:
35B10 Periodic solutions to PDEs
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Cesari, L., Existence in the large of periodic solutions of hyperbolic partial differential equations. Arch. Rational Mech. Anal. 20, 170–190 (1965). · Zbl 0154.35902
[2] Hale, J. K., Periodic solutions of a class of hyperbolic equations containing a small parameter. Arch. Rational Mech. Anal. 23, 380–398 (1967). · Zbl 0152.10002
[3] Vejvoda, O., Periodic solutions of a linear and weakly nonlinear wave equation in one dimension. I. Czech. Math. J. 14, 341–382 (1964). · Zbl 0178.45302
[4] Rabinowitz, P. H., Periodic solutions of nonlinear hyperbolic partial differential equations. Comm. Pure Appl. Math. 20, 145–205 (1967). · Zbl 0152.10003
[5] Rabinowitz, P. H., Periodic solutions of nonlinear hyperbolic partial differential equations. II. Comm. Pure Appl. Math. XXII, 15–39 (1969). · Zbl 0157.17301
[6] Havlova, J., Periodic solutions of a nonlinear telegraph equation. Casopis Pest. Mat. 90, 273–289 (1965), Prague. · Zbl 0143.13601
[7] Solovieff, P. V., Sur les solutions périodiques de certaines équations non-linéaires du quatrième ordre. Comptes Rendus (Doklady) de l’Académie de Sciences de l’URSS Vol. XXV, No. 9, 731–734 (1939). · JFM 65.1283.02
[8] Karimov, D. H., On the periodical solutions of nonlinear equations of the fourth order. Comptes Rendus (Doklady) de l’Académie des Sciences de l’URRS XLIX, 618–621 (1945). · Zbl 0061.22203
[9] Browder, F. E., Existence of periodic solutions for nonlinear equations of evolution. Proc. Nat. Acad. Sci. 53, 1272–1276 (1965). · Zbl 0125.35801
[10] Keller, J. B., & Lu Ting, Periodic vibrations of systems governed by non-linear partial differential equations. Comm. Pure Appl. Math. 19, 371–420 (1966). · Zbl 0284.35004
[11] Sethna, P. R., Free vibrations of beams with nonlinear viscoelastic material properties, Proceedings of the Fourth U.S. National Congress of Applied Mechanics, Amer. Society of Mech. Engineers, 1103–1112.
[12] Vejvoda, O., Nonlinear boundary value problems for differential equations: Differential Equations and their Applications, Czech. Acad. Sci., Prague, 199–215 (1963). · Zbl 0196.40102
[13] Cesari, L., Functional analysis and Galerkin’s method. Mich. Math. Jour. 11, 385–414 (1964). · Zbl 0192.23702
[14] Bancroft, S., J. K. Hale, & D. Sweet, Alternative problems for nonlinear functional equations. Jour. of Diff. Equations 4, 40–56 (1968). · Zbl 0159.20001
[15] Hall, W. S., On the existence of periodic solutions for the equations 322-01. Journal of Diff. Equations 7, 509–526 (1970). · Zbl 0198.14002
[16] Volevich, L. R., & B. P. Paneyakh, Certain spaces of generalized functions and embedding theorems. Russian Math. Surveys 20, 1–73 (1965). · Zbl 0135.16501
[17] Hobson, E. W., The Theory of Functions of a Real Variable and the Theory of Fourier Series. New York: Dover 1957, Vol. II, Chapter VIII, 599–605.
[18] Schwartz, L., Théorie des Distributions. Paris: Hermann 1966, Chapter VII, 1, 224–231.
[19] Bers, L., F. John, & M. Schechter, Partial Differential Equations. New York: Interscience 1964, Part II, Chapter 3, 164–189. · Zbl 0126.00207
[20] Edwards, R. E., Fourier Series: A Modern Introduction. New York: Holt, Rinehart, and Winston, Vol. II, 1967, Ch. 12, 46–132.
[21] Kantorovich, L.V., & G. P. Akilov, Functional Analysis in Normed Spaces. New York: MacMillan 1964, Chapter XVII, 4, 684–689. · Zbl 0127.06104
[22] Strauss, W. A., On the solutions of abstract nonlinear equations. Proc. Amer. Math. Soc. 18, 116–119 (1967). · Zbl 0144.17804
[23] Nirenberg, L., Remarks on strongly elliptic partial differential equations. Comm. Pure Appl. Math. 8, 648–674 (1955). · Zbl 0067.07602
[24] Moser, J., A rapidly convergent iteration method and nonlinear partial differential equations. Ann. Scuola Norm. Super. Pisa, Ser. 3, 20, 265–315 (1966). · Zbl 0144.18202
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.