| MR 0990299
| Zbl 0682.73036
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
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 , is used and the theory of M. S. Berger ,  and M. S. Berger and P. C. Fife  is adapted. This work is a part of .
 M. S. Berger P. C. Fife: Von Kármán's Equations and the Buckling of a Thin Elastic Plate, II Plate with General Edge Conditions
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 Ľ. Marko: Buckled States of Circular Plates. thesis, 1985 (Slovak).
 L. Nirenberg: Topics in Nonlinear Functional Analysis
. Russian translation, Mir, Moscow 1977. MR 0488104
| Zbl 0426.47034
 A. S. Voľmir: Elastic Plates and Shells. (Russian). GITTL, Moscow 1956.
 J. H. Wolkowisky: Existence of Buckled States of Circular Plates
. Comm. on Pure and Appl. Math. vol. XX, 1967, 549-560. MR 0213087
| Zbl 0168.45206