Geodesic
The number of buckled states of circular plates
Applications of Mathematics, Tome 34 (1989) no. 2, pp. 113-132

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This paper deals with the exact number of solutions of von Kármán equations for a rotationally symmetric buckling of a thin elastic plate. The plate of constant thickness is in static equilibrium under a uniform compressive thrust applied along its edge in the plane of the plate. The theory of M. G. Crandall, P. H. Rabinowitz [4], is used and the theory of M. S. Berger [1], [3] and M. S. Berger and P. C. Fife [2] is adapted. This work is a part of [6].
DOI : 10.21136/AM.1989.104340
Classification : 34B15, 35B32, 35J65, 37G99, 58E07, 58F14, 73C50, 73H05, 73K10, 74G60, 74K20
Keywords: Fredholm operator; static equilibrium; plate of constant thickness; Fredholm map of index zero; singular point; rotationally symmetric buckled states; von Kármán plate equations; operator equation; proper Sobolev space; local bifurcation behavior; nodal properties 
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     title = {The number of buckled states of circular plates},
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Marko, Ľubomír. The number of buckled states of circular plates. Applications of Mathematics, Tome 34 (1989) no. 2, pp. 113-132. doi: 10.21136/AM.1989.104340

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