Abstract
The global solvability of the problem about equilibrium of an elastic medium located in an elastic shell is established by variational methods. In the case of one-parametric force field, the bifurcation problem is studied. As is shown, the standard necessary condition for bifurcation is also sufficient for the problem under consideration. Bibliography: 7 titles.
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References
L. D. Landau and E. N. Lifshits, Elasticity Theory [in Russian], Nauka, Moscow (1965).
A. V. Pogorelov, Geometric Theory of Stability of Envelopes [in Russian], Nauka, Moscow (1966).
I. V. Skrypnik, Nonlinear Elliptic Equations of Higher Order, Kiev (1973).
I. V. Skrypnik, “Solvability and properties of solutions to nonlinear elliptic equations,” Recent Problems in Mathematics, VINITI, 9, 131–242 (1976).
D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, Berlin (1977).
P. Vyridis, “Bifurcation in a quasilinear variational problem on a one-dimensional manifold,” Probl. Mat. Anal. [in Russian], 22, 27–34 (2001); English transl.: J. Math. Sci., 106, No. 3, 2919–2924 (2001).
Ya. A. Roitberg and Z. G. Sheftel', “Theorem on diffeomorphisms for elliptic systems and its applications,” Mat. Sb. [in Russian], 78, No. 3, 446–472 (1969).
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Vyridis, P. Variational Problem on Equilibrium of an Elastic Medium Located in Elastic Shell. Journal of Mathematical Sciences 112, 3992–3996 (2002). https://doi.org/10.1023/A:1020097706989
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DOI: https://doi.org/10.1023/A:1020097706989