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The number of buckled states of circular plates. (English) Zbl 0682.73036
The paper deals with the determination of the exact number of solutions of rotationally symmetric buckled states of circular elastic plates. As governing equations the mechanical model of the von Kármán plate equations is selected. An abstract formulation of the problem as an operator equation in a proper Sobolev space is given. From this formulation theorems concerning the local bifurcation behavior and nodal properties of the solutions are derived.
Reviewer: H.Troger

MSC:
74G60 Bifurcation and buckling
35B32 Bifurcations in context of PDEs
34B15 Nonlinear boundary value problems for ordinary differential equations
74K20 Plates
35J65 Nonlinear boundary value problems for linear elliptic equations
37G99 Local and nonlocal bifurcation theory for dynamical systems
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References:
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[2] M. S. Berger P. C. Fife: Von Kármán’s Equations and the Buckling of a Thin Elastic Plate, II Plate with General Edge Conditions. Comm. on Pure and Appl. Math., vol. XXI, 1968, 227-241. · Zbl 0162.56501
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