References
Stakgold, I.: Branching of solutions of nonlinear equations. SIAM Review13, 289–332 (1971)
Schröder, J.: Störungsrechnung bei Eigenwert- und Verzweigungsaufgaben. Arch. Rat. Mech. Anal.1, 436–468 (1958)
Keller, H. B.: Nonlinear bifurcation. J. Diff. Eqs.7, 417–434 (1970)
Chen, Y. M., Christiansen, P. L.: Application of a modified newton's iteration method to construct solutions of eigenvalue problems of nonlinear partial differential operators. SIAM J. Appl. Math.18, 335–345 (1970)
Keller, H. B., Langford, W. F.: Iterations, perturbations and multiplicities for nonlinear Bifurcation problems. To appear in Arch. Rat. Mech. Anal.
Demoulin, Y. J., Chen, Y. M.: An iteration method for solving nonlinear eigenvalue problems. To appear in SIAM J. Appl. Math.
Keener, J. P., Keller, H. B.: Perturbed bifurcation theory. Submitted to Arch. Rat. Mech. Anal.
Kantorovich, L. V., Akilov, G. P.: Functional analysis in normed spaces. Oxford: Pergamon Press 1964
Nashed, M. Z.: Generalized inverse, normal solvability, and iteration for singular operator equations, in: Nonlinear functional analysis and applications, Ed. by L. B. Rall. New York: Academic Press 1971
Collatz, L.: Functional analysis and numerical mathematics. New York: Academic Press 1966
Minorsky, N.: Nonlinear oscillations, D. Princeton, N. J.: Van Nostrand Co., Inc. 1962
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Demoulin, YM.J., Chen, Y.M. An interation method for studying the bifurcation of solutions of the nonlinear equations,L(λ)u+ɛR(λ,u)=0. Numer. Math. 23, 47–61 (1974). https://doi.org/10.1007/BF01409990
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DOI: https://doi.org/10.1007/BF01409990