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A perturbation method applied to the buckling of a compressed elastica. (English) Zbl 0382.73032


MSC:

74G60 Bifurcation and buckling
47J05 Equations involving nonlinear operators (general)
47H99 Nonlinear operators and their properties
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[1] Berkey, D.; Freedman, M., A perturbation problem from control exhibiting on and off the boundary behavior, SIAM J. on control, 14, 857-876, (1976) · Zbl 0332.49008
[2] Freedman, M.; Granoff, B., The formal asymptotic solution of a singularly perturbed nonlinear optimal control problem, J. optimization theory appl., 19, 301-325, (1976) · Zbl 0307.49011
[3] FREEDMAN, M. and KAPLAN, J.; “Perturbation analysis of an optimal control problem involving bang-bang controls”, J. Differential Equations (to appear). · Zbl 0358.49011
[4] Keller, J.B.; Antman, S., Bifurcation theory and nonlinear eigenvalue problems, (1969), W.A. Benjamin New York · Zbl 0181.00105
[5] Reiss, E.L., Bifurcation theory and nonlinear eigenvalue problems, (1969), Benjamin New York · Zbl 0185.53002
[6] Reiss, E.L.; Matkowsky, N.J., Nonlinear dynamic buckling of a compressed elastic column, Quarterly of applied math., 245-260, (1971) · Zbl 0224.73064
[7] Stakgold, J., ()
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