Geodesic
Bifurcation theory of the time-dependent von Kármán equations
Applications of Mathematics, Tome 29 (1984) no. 1, pp. 3-13
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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.
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.
DOI : 10.21136/AM.1984.104063
Classification : 45D05, 45G10, 45M10, 73F15, 73K10, 74Hxx
Keywords: existence; bifurcation; nonlinear homogeneous Volterra integral equation; von Kármán equations; stability; rectangular visco-elastic plate 
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Brilla, Igor. Bifurcation theory of the time-dependent von Kármán equations. Applications of Mathematics, Tome 29 (1984) no. 1, pp. 3-13. doi: 10.21136/AM.1984.104063

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[2] N. Distéfano: Nonlinear Processes in Engineering. Academic press, New York, London 1974. | MR

[3] A. N. Kolmogorov S. V. Fomin: Elements of the theory of functions and functional analysis. (Russian). Izd. Nauka, Moskva 1976. | MR

[4] J. L. Lions: Quelques méthodes de résolution des problèmes aux limites no linéaires. Dunod, Gautier-Villars, Paris 1969. | MR

[5] F. G. Tricomi: Integral equations. Interscience Publishers, New York, 1957. | MR | Zbl

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