References
L. Bauer, H.B. Keller & E. L. Reiss, “Axisymmetric buckling of hollow spheres and hemispheres,” Comm. Pure Appl. Math. 23 (1970), 529–568.
M.S. Berger & P.C. Fife, “On von Kármán's equations and the buckling of a thin elastic plate,” Bull. Amer. Math. Soc. 72 (1966), 1006–1011.
M.S. Berger, “On the existence of equilibrium states of thin elastic shells (I),” Indiana Math. J. 20 (1971), 591–602.
R. Courant & D. Hilbert, “Methods of Mathematical Physics,” vol. I, Interscience Publishers, New York, 1953.
G.H. Knightly & D. Sather, “Nonlinear axisymmetric buckling of shallow spherical caps,” SIAM J. Math. Anal. 6 (1975), 913–924.
W.T. Koiter, “The nonlinear buckling problem of a complete spherical shell under uniform external pressure,” Proc. Kon. Nederl. Akad. Wet. Amsterdam B72 (1969), 40–123.
C.G. Lange & G. A. Kriegsmann, “The axisymmetric branching behavior of complete spherical shells,” preprint, 1974.
H.E. Rauch, “Instability of thin-walled spherical structures under external pressure,” Contributions to Analysis, Academic Press, New York, 1974, 357–373.
E. Reissner, “On the axisymmetrical deformation of thin shells of revolution,” Proc. Symposia in Appl. Math. 3 (1950), 27–52.
E.H. Rothe, “Completely continuous scalars and variational methods,” Ann. of Math. 49 (1948), 265–278.
D. Sather, “Bifurcation and stability for a class of shells,” Arch. Rational Mech. Anal., 63 (1976), 295–304.
D. Sather, “Branching of solutions of nonlinear equations,” Proc. Seminar on Nonlinear Eigenvalue Problems, Santa Fe, 1971, Rocky Mtn. J. Math. 3 (1973), 203–250.
D. Sather, “Branching of solutions of an equation in Hubert space,” Arch. Rational Mech. Anal. 36 (1970), 47–64.
D.H. Sattinger, “Stability of bifurcating solutions by Leray-Schauder degree,” Arch. Rational Mech. Anal. 43 (1971), 154–166.
I. Stakgold, “Branching of solutions of nonlinear equations,” SIAM Review 13 (1971), 289–332.
J.M.T. Thompson, “The rotationally-symmetric branching behavior of a complete spherical shell,” Proc. Kon. Nederl. Akad. Wet. Amsterdam B67 (1964), 295–311.
J.M.T. Thompson & G. W. Hunt, “A General Theory of Elastic Stability,” John Wiley and Sons, London, 1973.
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Communicated by J.B. McLeod
The research of G. H. Knightly reported here was supported in part by a grant from the U.S. National Science Foundation, No. MPS 75-07579; that of D. Sather was supported in part by U.S. National Science Foundation Grant No. MPS 73-08948 and in part by the Council on Research and Creative Work of the University of Colorado.
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Knightly, G.H., Sather, D. Existence and stability of axisymmetric buckled states of spherical shells. Arch. Rational Mech. Anal. 63, 305–319 (1976). https://doi.org/10.1007/BF00279990
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DOI: https://doi.org/10.1007/BF00279990