References
Antman, S. S., The eversion of thick spherical shells, Arch. Rational Mech. Anal. 70, 113–123, 1979.
Antman, S. S., & Negron-Marrero, P. V., The remarkable nature of radially symmetric equilibrium states of aeolotropic nonlinearly elastic bodies, J. Elast. 18, 131–164, 1987.
Bartle, R. G., The Elements of Real Analysis, Wiley, New York, 1964.
Bluman, G. W., & Cole, J. D., Similarity Methods for Differential Equations, Springer-Verlag, New York, 1974.
Buzano, E, Geymonat, G., & Poston, T., Post-buckling behavior of a non-linearly hyperelastic thin rod with cross-section invariant under the dihedral group D n ,Arch. Rational Mech. Anal. 89, 307–388, 1985.
Dieudonné, J., Foundations of Modern Analysis, Academic Press, New York, 1969.
Ericksen, J. L., Special topics in elastostatics, in Advances in Applied Mechanics, ed. C.-S. Yih, 17, 189–244, 1977.
Golubitsky, M., The Benard problem, symmetry and the lattice of isotropy sub-groups, in Bifurcation Theory, Mechanics and Physics, ed. C. P. Borter et al., Reidel, Dordrecht, 225–256, 1983.
Gurtin, M. E., An Introduction to Continuum Mechanics, Academic Press, New York, 1981.
Healey, T. J., A group-theoretic approach to computational bifurcation problems with symmetry, Comput. Meth. Appl. Mech. Engng, 67, 257–295, 1988.
Healey, T. J., Global bifurcation and continuation in the presence of symmetry with an application to solid mechanics, SIAM J. Math. Anal. 19, 824–840, 1988.
Knightly, G. A., & Sather, D., Buckled states of a spherical shell under uniform external pressure, Arch. Rational Mech. Anal. 72, 315–380, 1980.
Lie, S., Differentialgleichungen, Chelsea Publishing Company, New York, 1967 (reprint).
Miller, W., Symmetry Groups and Their Applications, Academic Press, New York 1972.
Muncaster, R. G., An abstract approach to group invariance with applications to differential equations, Arch. Rational Mech. Anal. 78, 1–28, 1982.
Necas, J., Les Méthodes Directes en Théorie des Equations Elliptiques, Masson, Paris, 1967.
Olver, P. J., Applications of Lie Groups to Differential Equations, Springer-Verlag, New York, 1986.
Sattinger, D. H., Group Theoretic Methods in Bifurcation Theory, Springer-Verlag, New York, 1979.
Sattinger, D. H., Bifurcation and symmetry breaking in applied mathematics, Bull. Amer. Math. Soc. 3, 779–819, 1980.
Schensted, I. V., A Course on the Applications of Group Theory to Quantum Mechanics, NEO Press, Peaks Island, Maine, 1976.
Sirotin, Y. I., & Shaskolskaya, M. P., Fundamentals of Crystal Physics, Mir Publishers, Moscow, 1982.
Truesdell, C., & Noll, W., The Nonlinear Field Theories of Mechanics, in Handbuch der Physik, Vol. III/3 ed. S. Flügge, Springer-Verlag, (1965).
Vanderbauwhede, A., Generic bifurcation and symmetry, with an application to the von Karman equations, Proc. Roy, Soc. Edinburgh 81A, 211–235, 1978.
Vanderbauwhede, A., Local Bifurcation and Symmetry, Pitman, Boston, 1982.
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Communicated by R. G. Muncaster
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Healey, T.J. Symmetry and equivariance in nonlinear elastostatics, Part I. Arch. Rational Mech. Anal. 105, 205–228 (1989). https://doi.org/10.1007/BF00251500
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DOI: https://doi.org/10.1007/BF00251500