References
Alexander, J. A., & J. Yorke, Global bifurcation of periodic orbits. U. of Maryland report (1974).
Bauer, L., & E. Reiss, Nonlinear buckling of rectangular plates. SIAM J. 13, 603–626 (1965).
Bauer, L., E. Reiss & H. Keller, Multiple eigenvalues lead to secondary bifurcation. SIAM Review 17 (1975).
Berger, M., & P. Fife, On von Kármán's equations and the buckling of a thin elastic plate. II. Plate with general edge conditions. Comm. Pure Appl. Math. 21, 227–241 (1968).
Chafee, N., The bifurcation of one or more closed orbits from an equilibrium point of an autonomous differential system. J. Differential Equations 4, 661–679 (1968).
Chow, S., J. K. Hale, & J. Mallet-Paret, Applications of generic bifurcation. I. Arch. Rational Mech. Anal. 59, 159–188 (1975).
Chow, S., & J. Mallet-Paret, Integral averaging and bifurcation. To appear.
Chow, S., & J. Mallet-Paret, Fuller's index and global Hopf bifurcation. To appear.
Crandall, M. G., & P. Rabinowitz, Bifurcation from simple eigenvalues. J. Funct. Anal. 8, 321–340(1971).
Dancer, E., Bifurcation theory in real Banach space. Proc. London Math. Soc. 23, 699–734 (1971).
Dancer, E., Bifurcation theory for analytic operators. Proc. London Math. Soc. 26, 359–384 (1973).
Dancer, E., Global structure of the solutions of nonlinear real analytic eigenvalue problems. Proc. London Math. Soc. 27, 747–765 (1973).
Golubitsky, M., & V. Guillemin, Stable Mappings and Their Singularities. New York: Springer 1973.
Greenlee, W. M., Remarks on branching from multiple eigenvalues, pp. 101–122, Lecture notes in Math. Vol. 322. Springer-Verlag, New York, 1973.
Hopf, E., Abzweigung einer periodischen Lösung von einer stationären Lösung eines Differential systems. Ber. Math.-Phys. Sächsische Akademie der Wissenschaften Leipzig 94, 1–22 (1942).
Ize, J., Bifurcacion global de orbitas periodicas. To appear.
Keener, J., Perturbed bifurcation theory at multiple eigenvalues. Arch. Rational Mech. Anal. 56, 348–366 (1974).
Keener, J., & H. Keller, Perturbed bifurcation theory. Arch. Rational Mech. Anal. 50, 159–175 (1973).
Kirchgässner, K., Multiple eingenvalue bifurcation for holomorphic mappings, pp. 69–99. Contributions to Nonlinear Functional Analysis. Ed. by E. H. Zarantonello. New York: Academic Press 1971.
Knightly, G. H., & D. Sather, Nonlinear buckled states of rectangular plates. Arch. Rational Mech. Anal. 54, 356–372 (1974).
Knightly, G. H., & D. Sather, On nonuniqueness of solutions of the von Kármán equations. Arch. Rational Mech. Anal. 36, 65–78 (1970).
Koiter, W. T., Over de stabiliteit van het elastich evenwicht. Thesis Delft. H. J. Paris, Amsterdam (1945); Eng. Transl. Tech. Rpt. AFFDL-TR-70-25, Feb. 1970.
Koiter, W. T., Elastic stability and post-buckling behavior, pp. 257–275. Nonlinear Problems, ed. by R. Langer, Univ. Wisc. Press, 1963.
Krasnoselskii, M. A., Topological Methods in the Theory of Nonlinear Integral Equations. New York: MacMillan 1964.
Matkowsky, B., & L. Putnik, Multiple buckled states of rectangular plates. Int. J. Nonlinear Mech. 9, 89–103 (1974).
MacLeod, J. B., & D. H. Sattinger, Loss of stability at a double eigenvalue. J. Funct. Anal. 14, 62–84 (1973).
Rabinowitz, P., Some global results on nonlinear eigenvalue problems. J. Funt. Anal. 7, 487–513 (1971).
Sather, D., Branching of solutions of nonlinear equations. Rocky Mountain J. Math. 3, 203–250 (1973).
Thom, R., Structural Stability and Morphogenesis. Amsterdam: Benjamin 1975. Translation from French.
Vainberg, M. M., & V. A. Trenogin, Theory of Branching of Solutions of Nonlinear Equations. Leiden: Nordhoff 1974.
Wassermann, G., Stability of Unfoldings, Lecture notes in Math. vol. 393. Berlin-Heidelberg New York: Springer 1974.
Westreich, D., Banach space bifurcation theory. Trans. A.M.S. 171, 135–156 (1973).
Zachman, D., Branching solutions of equations containing several parameters. SIAM J. Math. Anal. 5, 898–907 (1974).
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Communicated by C. Dafermos
This research was supported in part by the U. S. National Science Foundation under GP-28931 X2, in part by the United States Army, Durham, under DA-ARO-D-31-124-73-G-130 and in part by the Air Force Office of Scientific Research under AF-AFOSR 71-2078 C.
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Chow, SN., Hale, J.K. & Mallet-Paret, J. Applications of generic bifurcation. II. Arch. Rational Mech. Anal. 62, 209–235 (1976). https://doi.org/10.1007/BF00280015
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DOI: https://doi.org/10.1007/BF00280015