Article
MSC:
45D05,
45G10,
45M10,
73F15,
73K10,
74Hxx | MR 0729948 | Zbl 0538.45006 | DOI: 10.21136/AM.1984.104063
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Keywords:
existence; bifurcation; nonlinear homogeneous Volterra integral equation; von Kármán equations; stability; rectangular visco-elastic plate
existence; bifurcation; nonlinear homogeneous Volterra integral equation; von Kármán equations; stability; rectangular visco-elastic plate
Summary:
In this paper the author studies existence and bifurcation of a nonlinear homogeneous Volterra integral equation, which is derived as the first approximation for the solution of the time dependent generalization of the von Kármán equations. The last system serves as a model for stability (instability) of a thin rectangular visco-elastic plate whose two opposite edges are subjected to a constant loading which depends on the parameters of proportionality of this boundary loading.
References:
[1] J. Brilla: Stability problems in mathematical theory of viscoelasticity. in Equadiff IV, Proceedings, Prague, August 22-26, 1977 (ed. J. Fabera). Springer, Berlin-Heidelberg- New York 1979. MR 0535322
[2] N. Distéfano: Nonlinear Processes in Engineering. Academic press, New York, London 1974. MR 0392042
[3] A. N. Kolmogorov S. V. Fomin: Elements of the theory of functions and functional analysis. (Russian). Izd. Nauka, Moskva 1976. MR 0435771
[4] J. L. Lions: Quelques méthodes de résolution des problèmes aux limites no linéaires. Dunod, Gautier-Villars, Paris 1969. MR 0259693
[5] F. G. Tricomi: Integral equations. Interscience Publishers, New York, 1957. MR 0094665 | Zbl 0078.09404
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