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perturbed; unperturbed cases; Signorini problem; bifurcations; simply supported rod; axially loaded; least rotation; lateral displacements; nonlinear differential equations; potential energies; equilibrium configurations; buckling of the rod; variational inequality
A unilateral boundary-value condition at the left end of a simply supported rod is considered. Variational and (equivalent) classical formulations are introduced and all solutions to the classical problem are calculated in an explicit form. Formulas for the energies corresponding to the solutions are also given. The problem is solved and energies of the solutions are compared in the pertubed as well as the unperturbed cases.
[1] E. L. Reiss: Column buckling- an elementary example of bifurcation. In: Bifurcation Theory and Nonlinear Eigenvalue Problems, ed. by J. B. Keller and S. Antman, p. 1-16, New York, Benjamin, 1969. MR 0241213 | Zbl 0185.53002
[2] А. А. Березовский: Лекции хо нелинейным краевым задачам математической физики. Наукова думка, 1976. Zbl 1160.26301
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