Abstract
Some ideas on bifurcation problems with several parameters are collected an different phenomena are illustrated on examples of bifurcation problems which one can sole explicitely. The examples are dealing not only with differential equations but also with other fields.
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References
[72] Atkinson, F.V.: Multiparameter Eigenvalue Problems in Vol. I: Matrices and Compact Operators, Academic Press, New York, 1972.
[73] Berge, Cl.: Graphs and Hypergraphs, Nord Holland Publ. Comp., 1973, 528 S.
[80] Browne, P.J. and B.D. Sleeman: Applications of multiparameter spectral theory to special functions, Math. Proc. Camb. Phil. Soc. (1980) 87, 275–283.
[63] Collatz, L.: Eigenwertaufgaben mit technischen Anwendungen, Leipzig 1963.
[68] Collatz, L.: Multiparametric Eigenvalue Problems in Inner-product Spaces, Journ. Computer System Sciences 2 (1968), 333–341.
[76] Collatz, L.: Bifurcation diagrams, Proc. Conference Diff. Equat. Dundee, 1976, Springer Lecture Notes in Math. 564 (1976) 41–53.
[77] Collatz, L.: Verzweigungsdiagramme und Hypergraphen, Internat.Ser.Num.Math. 38 (1977), 9–42.
[77] Dickey, R.W.: Bifurcation problems in nonlinear elasticity Pitman 1977, 119 p.
[66] Gut, J.: Kipp-Probleme als zusammengesetzte Stabilitätsaufgaben, Schweizerische Bauzeitung 84 (1966), p. 38–41.
[67] Hadeler, K.P.: Mehrparametrige und nichtlineare Eigenwertaufgaben, Archive Rat.Math.Mech 27 (1967), 306–328.
[74] Sleeman, B.D.: Left-definite multiparameter eigenvalue problems, in "Proceedings, Symposium on Spectral Theory and Differential Equations," pp. 307–321, Lecture Notes in Mathematics, No. 488, Springer-Verlag, Berlin, 1974.
[79] Sleeman, B.D.: Klein Oscillation theorems for multiparameter eigenvalue problems in ordinary differential equations, Nieuw archief voor wiskunde (3), 27 (1979), 341–362.
[71] Stakgold, I.: Branching of Solutions of nonlinear Equations, SIAM REVIEW 13 (1971) 289–332.
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© 1981 Springer-Verlag
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Collatz, L. (1981). Remark on bifurcation problems with several parameters. In: Everitt, W.N., Sleeman, B.D. (eds) Ordinary and Partial Differential Equations. Lecture Notes in Mathematics, vol 846. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0089827
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DOI: https://doi.org/10.1007/BFb0089827
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