Dancer, E. N.
A new degree for S 1 -invariant gradient mappings and applications
Annales de l'I.H.P. Analyse non linéaire, Tome 2 (1985) no. 5 , p. 329-370
Zbl 0579.58022 | MR 817033 | 1 citation dans Numdam
URL stable : http://www.numdam.org/item?id=AIHPC_1985__2_5_329_0

Bibliographie

[1] R. Abraham and J. Robbins, Transversal mappings and flows, Reading, Benjamin, 1967. MR 240836 | Zbl 0171.44404

[2] S. Agmon, Lectures on elliptic boundary-value problems, Princeton, Van Nostrand, 1965. MR 178246 | Zbl 0142.37401

[3] J.C. Alexander and J. Yorke, Global bifurcation of periodic orbits, Amer. J. Math., t. 100, 1978, p. 263-292. MR 474406 | Zbl 0386.34040

[4] H. Amann and E. Zehnder, Non-trivial solutions for a class of non-linear differential equations, Ann. Scuola Norm Sup Pisa, t. 7, 1980, p. 539-693. Numdam | MR 600524 | Zbl 0452.47077

[5] M.S. Berger, Nonlinearity and functional analysis, New York, Academic Press, 1977. MR 488101 | Zbl 0368.47001

[6] J. Bochnak and J. Siciak, Analytic functions in topological vector spaces, Studia Math., t. 39, 1971, p. 77-111. MR 313811 | Zbl 0214.37703

[7] R. Bohme, Die Losung der Verzweignungsgleichugen für nichtlineare Eigenwert-probleme, Math. Z., t. 127, 1972, p. 105-126. MR 312348 | Zbl 0254.47082

[8] G. Bredon, Introduction to compact transformation groups, New York, Academic Press, 1972. MR 413144 | Zbl 0246.57017

[9] H. Brezis, Opérateurs maximaux monotones, Amsterdam, North Holland, 1973. MR 348562

[10] S. Chow and J. Mallet-Paret, The Fuller index and global bifurcation, J. Diff. Eqns., t. 29, 1978, p. 66-85. MR 492560 | Zbl 0369.34020

[11] S.N. Chow, J. Mallet-Paret and J. Yorke, Global Hopf bifurcation from a multiple eigenvalue, Nonlinear Analysis, t. 2, 1978, p. 753-763. MR 512165 | Zbl 0407.47039

[12] C. Conley, Isolated invariant sets and the Morse Index, CBMS regional conferences in mathematics, no. 38, Providence, Amer. Math. Soc., 1978. MR 511133 | Zbl 0397.34056

[13] M. Crandall and P.H. Rabinowitz, Bifurcation from simple eigenvalues, J. Functional Anal., t. 8, 1971, p. 321-340. MR 288640 | Zbl 0219.46015

[14] E.N. Dancer, Bifurcation in real Banach space, Proc. London Math. Soc., t. 23, 1971, p. 699-734. MR 305166 | Zbl 0227.47050

[15] E.N. Dancer, Global solution branches for positive mappings, Archives Rat. Mech. Anal., t. 52, 1973, p. 181-192. MR 353077 | Zbl 0275.47043

[16] E.N. Dancer, The G-invariant implicit function theorem in infinite-dimensions, Proc. Royal Soc. Edinburgh, t. 92 A, 1982, p. 13-30. MR 667122 | Zbl 0512.58011

[17] E.N. Dancer, An implicit function theorem with symmetries and its application to nonlinear eigenvalue problems, Bull. Austral. Math. Soc., t. 21, 1980, p. 81-91. MR 569089 | Zbl 0414.58012

[18] E.N. Dancer, On the structure of solutions of an equation in catalysis theory when a parameter is large, J. Diff. Eqns., t. 39, 1980, p. 404-437. MR 590000 | Zbl 0417.34042

[19] E.N. Dancer, On non-radially symmetric bifurcation, J. London Math. Soc., t. 20, 1979, p. 287-292. Zbl 0418.35015

[20] E.N. Dancer, On the structure of solutions of nonlinear eigenvalue problems, Indiana Univ. Math. J., t. 23, 1974, p. 1069-1076. MR 348567 | Zbl 0276.47051

[21] E.N. Dancer, Perturbation of zeros in the presence of symmetries, to appear in J. Austral. Math. Soc. MR 720004 | Zbl 0535.58013

[22] E.N. Dancer, Remarks on S1-symmetries and a special degree for S1-invariant gradient mappings, submitted.

[23] E.N. Dancer, Degenerate critical points, homotopy indices and Morse inequalities, J. Reine Ang. Math., t. 350, 1984, p. 1-22. MR 743531 | Zbl 0525.58012

[24] E. Fadell and R. Rabinowitz, Generalized cohomology theories for Lie group actions with an application to bifurcation questions for Hamiltonian systems, Invent. Math., t. 45, 1978, p. 139-174. MR 478189 | Zbl 0403.57001

[25] I. Gokhberg, P. Lancaster and L. Rodman, Perturbation of H-self-adjoint matrices with applications to differential equations, Integral equations and operator theory, t. 5, 1982, p. 718-757. MR 697011 | Zbl 0511.15010

[26] J. Ize, Bifurcation theory for Fredholm operators, Mem. Amer. Math. Soc., t. 174, 1976. MR 425696 | Zbl 0338.47032

[27] T. Kato, Perturbation theory for linear operators, Berlin, Springer, 1966. Zbl 0148.12601

[28] N. Lloyd, Degree theory, Cambridge, Cambridge University Press, 1978. MR 493564 | Zbl 0367.47001

[29] J. Logan, Invariant variational principles, New York, Academic Press, 1977. MR 500376

[30] R. Magnus, A generalization of multiplicity and the problem of bifurcation, Proc. London Math. Soc., t. 32, 1976, p. 251-278. MR 402561 | Zbl 0316.47042

[31] R. Narasimhan, Lectures on topics in analysis, Bombay, Tata Institute, 1965. MR 212837 | Zbl 0185.33601

[32] R. Nussbaum, The fixed point index for locally condensing maps, Ann. Mat. Pura Appl., t. 89, 1971, p. 217-258. MR 312341 | Zbl 0226.47031

[33] P.H. Rabinowitz, Some global results for nonlinear eigenvalue problems, J. Funct. Anal., t. 7, 1971, p. 487-513. MR 301587 | Zbl 0212.16504

[34] P.H. Rabinowitz, A bifurcation theorem for potential operators, J. Funct. Anal., t. 25, 1977, p. 412-424. MR 463990 | Zbl 0369.47038

[35] D. Sattinger, Group theoretic methods in bifurcation theory, Lecture notes in mathematics, no. 762, Berlin, Springer, 1979. MR 551626 | Zbl 0414.58013

[36] C. Siegel and J. Moser, Lectures on celestial mechanics, Berlin, Springer-Verlag, 1971. MR 502448 | Zbl 0312.70017

[37] M. Vainberg, Variational methods for the study of nonlinear equations, San Francisco, Holden-Day, 1964.

[38] G. Wasserman, Equivariant differential topology, Topology, t. 8, 1969, p. 127-150. MR 250324 | Zbl 0215.24702

[39] P. Wolfe, Equilibrium states of an elastic conductor in a magnetic field: a paradigm of bifurcation theory, Trans. Amer. Math. Soc., t. 278, 1983, p. 377-388. MR 697082 | Zbl 0519.73093

[40] P. Wolfe, Rotating states of an elastic conductor, preprint. MR 826837