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Perturbed bifurcation theory. (English) Zbl 0254.47080

MSC:
47J05 Equations involving nonlinear operators (general)
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[1] Dean, E. T., & P. L.Chambré, Branching of solutions of some nonlinear eigenvalue problems. J. Math. Phys.11, 1567-1574 (1970). · Zbl 0191.11902 · doi:10.1063/1.1665295
[2] Dean, E. T., & P. L.Chambré, On the solutions of the nonlinear eigenvalue problem 175-01. Bull. Amer. Math. Soc.76, 595-600 (1970). · Zbl 0206.40502 · doi:10.1090/S0002-9904-1970-12450-8
[3] Keener, J. P., Buckling imperfection sensitivity for columns and spherical caps. Quart. Appl. Math. (to appear). · Zbl 0284.73029
[4] Keener, J. P., Some modified bifurcation problems with application to imperfection sensitivity in buckling. Ph. D. thesis, California Institute of Technology, Pasadena, California 1972.
[5] Keener, J. P., & H. B.Keller, Perturbed bifurcation and buckling of circular plates, Conference on Ordinary and Partial Differential Equations, University of Dundee. Lecture Notes in Mathematics280, 286-293. Berlin Heidelberg New York: Springer 1972. · Zbl 0254.73044
[6] Keener, J. P., & H. B.Keller, Positive solutions of convex nonlinear eigenvalue problems. J. Diff. Eqs. (to appear). · Zbl 0287.35074
[7] Keller, H. B., & W. F.Langfrod, Iterations, perturbations and multiplicities in nonlinear bifurcation problems. Arch. Rational Mech. Anal.43, 83-108 (1972). · Zbl 0249.47058
[8] Krasnosel’skii, M. A., Topological Methods in the Theory of Nonlinear Integral Equations. Oxford: Pergamon Press 1964.
[9] Laetsch, T. W., Eigenvalue problems for positive monotonic nonlinear operators. Ph. D. thesis, California Institute of Technology, Pasadena, California 1969.
[10] Sather, D., Branching of solutions of an equation in Hilbert space. Arch. Rational Mech. Anal.36, 47-64 (1970). · Zbl 0189.14902 · doi:10.1007/BF00255746
[11] Vainberg, M. M., & V. A.Trenogin, The methods of Lyapunov and Schmidt in the theory of nonlinear equations and their further development. Russian Math. Surveys17, No. 2, 1-60 (1962). · Zbl 0117.31904 · doi:10.1070/RM1962v017n02ABEH001127
[12] Westreich, D., Bifurcation theory in a Banach space. Ph. D. thesis, Yeshiva Univ., New York City, N.Y. 1971. · Zbl 0219.47059
[13] Malkin, I. G., Some problems in the theory of nonlinear oscillations. State Pub. House of Tech. and Theory Lit., Moscow (1956); English translation AEC-tr-3766 (Book 1, Book 2), U.S. Dept. of Comm., N.B.S., Inst. for Applied Tech. 1959.
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