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On the genericity of a bifurcation point of infinite type and multiple solutions of an elastic membrane. (English) Zbl 0812.73026
An interesting question in bifurcation theory of static systems is whether in a global bifurcation diagram by an appropriate perturbation all more complicated bifurcations than limit points can be made to dissolve in such a manner that only limit points remain. In a paper by A. J. Callegari, E. L. Reiss and H. B. Keller [Commun. Pure Appl. Math. 24, 499-527 (1971; Zbl 0218.73061)] the answer is shown to be negative by means of the physical example of an edge-loaded membrane.
The author of the present paper gives a nice generalization of this result for more general types of loadings by means of a completely different mathematical approach compared to the paper mentioned above.
Reviewer: H.Troger (Wien)
MSC:
74G60 Bifurcation and buckling
74K20 Plates
34C23 Bifurcation theory for ordinary differential equations
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References:
[1] Golubitsky, M.; Schaeffer, D., Singularities and groups in bifurcation theory I, (1985), Springer New York · Zbl 0607.35004
[2] Callegari, A.J.; Reiss, E.L., Nonlinear boundary value problems for the circular membrane, Archs ration. mech. analysis, 31, 390-400, (1970) · Zbl 0179.54406
[3] Callegari, A.J.; Keller, H.B.; Reiss, E.L., Membrane buckling: a study of solution multiplicity, Communs pure appl. math., 24, 499-521, (1971) · Zbl 0208.26801
[4] Dickey, R.W., The plane circular elastic surface under normal pressure, Archs ration. mech. analysis, 26, 219-236, (1967) · Zbl 0166.43504
[5] Yoshizawa, T., Stability theory and the existence of periodic and almost periodic solutions, (1975), Springer New York · Zbl 0304.34051
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