Abstract
Let W and Y be real Banach spaces and F:W → Y be a smooth mapping. Let xɛW be a solution of F(z)=0, Bifurcation theory deals with the problem of determining the structure of the zeros of F near x. We give a modification of a well-known theorem of Crandall and Rabinowitz which is useful for applications, i.e. for the computation of bifurcation points. A numerical example is included.
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Literatur
CRANDALL, M.G., RABINOWITZ, P.H.: Bifurcation from simple eigenvalues, J. Functional Anal.8, 321–340 (1971)
RHEINBOLDT, W.C.: Numerical methods for a class of finite-dimensional bifurcation problems, SIAM J. Nuraer. Anal.15, 1–11 (1978)
WEBER, H.: Numerische Behandlung von Verzweigungs-problemen bei gewöhnlichen Randwertaufgaben, in: ALBRECHT, J., COLLATZ, L., KIRCHGÄSSNER, K. (eds.): Constructive methods for nonlinear boundary value problems and nonlinear oscillations, ISNM vol. 48, S. 176–190, Birkhäuser, Basel 1979
WEBER, H.: On the numerical approximation of secondary bifurcation problems, in: PEITGEN, H.O. (ed.): Numerical solution of nonlinear equations, Lecture Notes in Mathematics, Springer, Berlin 1981
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Weber, H. Zur Verzweigung bei einfachen Eigenwerten. Manuscripta Math 38, 77–86 (1982). https://doi.org/10.1007/BF01168387
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DOI: https://doi.org/10.1007/BF01168387