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Title: An existence theorem for the v. Kármán equations under the condition of free boundary (English)
Author: Naumann, Joachim
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 19
Issue: 1
Year: 1974
Pages: 17-27
Summary lang: English
Summary lang: Czech
Category: math
Summary: The paper concerns the v. Kármán equations governing the bending of a thin elastic plate under the condition of free boundary. Starting from the definition of a variational solution, the boundary value problem considered is replaced by an equivalent abstract operator equation to which the known theorems of the nonlinear operator theory apply. The main result consists in an existence theorem of a variational solution for the problem under consideration. ()
MSC: 35B45
MSC: 35D05
MSC: 35G20
MSC: 35Q99
idZBL: Zbl 0291.35011
idMR: MR0346294
DOI: 10.21136/AM.1974.103510
Date available: 2008-05-20T17:58:00Z
Last updated: 2020-07-28
Stable URL:
Reference: [1] Berger M. S., Fife P.: On von Karman's equations and the buckling of a thin elastic plate.11. Plate with general edge conditions. - Comm. Pure Appl. Math.,21 (1968), 227- 241. MR 0229978, 10.1002/cpa.3160210303
Reference: [2] Fife P.: Non-linear deflection of thin elastic plates under tension.- Comm. Pure Appl. Math., 14 (1961), 81 - 112. Zbl 0099.40802, MR 0128697, 10.1002/cpa.3160140202
Reference: [3] Knightly G. H.: An existence theorem for the von Kármán equations.- Arch. Rat. Mech. Anal., 27 (1967), 233 - 242. Zbl 0162.56303, MR 0220472, 10.1007/BF00290614
Reference: [4] Knightly G. H., Sather D.: On nonuniqueness of solutions of the von Kármán equations.- Arch. Rat. Mech. Anal., 36 (1970), 65-78. Zbl 0188.57603, MR 0261835, 10.1007/BF00255747
Reference: [5] Morozov N. F.: Nonlinear problems in the theory of thin plates.(Russian). - Vestnik Leningr. Univ., 19 (1958), 100-124. MR 0102224
Reference: [6] Nečas J.: Les méthodes directes en théorie des équations elliptiques.- Academia, Prague 1967. MR 0227584
Reference: [7] Sharij Ju. I., Jurchenko A. S.: Dirichleťs problem for equations of Karman's type.- Diff. urav., 4(1968), 1713-1719. MR 0235279


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