×

An existence theorem for the von Kármán equations. (English) Zbl 0162.56303


PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Bauer, F., & E. Reiss, Non-linear buckling of rectangular plates. J. Soc. Indust. Appl. Math. 13, 603-627 (1965).
[2] Berger, M., & P. Fife, On von Kármán’s equations and the buckling of a thin elastic plate. Bull. Amer. Math. Soc. 72, 1006-1011 (1966). (Details to appear in an article by M. Berger under the same title in Comm. Pure. Appl. Math.) · Zbl 0146.22103
[3] Edwards, J., On the existence of solutions of the steady-state Navier-Stokes equations for a class of non-smooth boundary data. Tech. Rep. No. 6-90-63-70. Sunnyvale, Calif.: Lockheed Missiles and Space Co. 1963.
[4] Fife, P., Non-linear deflection of thin elastic plates under tension. Comm. Pure Appl. Math. 14, 81-112 (1961). · Zbl 0099.40802
[5] Friedrichs, K., & J. Stoker, The non-linear boundary value problem of the buckled plate. Amer. J. Math. 63, 839-888 (1941). · Zbl 0026.16301
[6] Hopf, E., Ein allgemeiner Endlichkeitssatz der Hydrodynamik. Math. Ann. 117, 764-775 (1940-41). · Zbl 0024.13505
[7] Keller, H., J. Keller, & E. Reiss, Buckled states of circular plates. Quart. Appl. Math. 20, 55-65 (1962). · Zbl 0134.44602
[8] Keller, H., & E. Reiss, Iterative solutions for non-linear bending of circular plates. Comm. Pure Appl. Math. 11, 273-292 (1958). · Zbl 0081.18505
[9] Leray, J., Étude de diverses équations integrales non-linéaires et de quelques problèmes que pose l’hydrodynamique. J. Math. Pure Appl. 9, 1-82 (1933). · Zbl 0006.16702
[10] Leray, J., & J. Schauder, Topologie et équations fonctionelles. Ann. Sci. Ecole Norm. Supp. 51, 45-78 (1934). · JFM 60.0322.02
[11] Morosov, N., On the non-linear theory of thin plates. Dokl. Akad. Nauk SSSR 114, 968-971 (1957). · Zbl 0083.39904
[12] Schaefer, H., Über die Methode der a-priori Schranken. Math. Ann. 129, 415-416 (1955). · Zbl 0064.35703
[13] Sobolev, S., Applications of functional analysis in mathematical physics. Translations of mathematical monographs 7, Amer. Math. Soc. Providence 1963. · Zbl 0123.09003
[14] Kármán, T. v., Festigkeitsprobleme im Maschinenbau. Encyk. der Math. Wissenschaften IV-4. C, S. 348-352. Leipzig 1907-1914.
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.