References 1. R.A. Adams. Sobolev Spaces. Academic Press, San Diego-London, 1978. 2. S. Agmon. On the eigenfunctions and on the eigenvalues of general elliptic boundary value problems. Communications on Pure and Applied Mathematics, 15:119-147,1962. 3. J.C. Alexander and J.A. Yorke. Global bifurcation of periodic orbits. American Journal of Mathematics, 100:263-292, 1978. 4. E.L. Allgower and K. Georg. Numerical Continuation Methods. An Introduc- tion. Springer-Verlag, Berlin-Heidelberg-New York, 1990. 5. H. Amann. Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces. SIAM Review, 18:620-709, 1976. 6. H. Amann. Ordinary Differential Equations. de Gruyter, Berlin, 1990. 7. H. Amann. Linear and Quasilinear Parabolic Problems. Volume I: Abstract Linear Theory. Birkhiiuser, Basel-Boston-Berlin, 1995. 8. H. Amann and S. Weiss. On the uniqueness of the topological degree. Mathe- matische Zeitschrijt, 130:39-54, 1973. 9. A. Ambrosetti. Branching points for a class of variational operators. Journal d'Analyse Mathematique, 76:321-335, 1998. 10. A. Ambrosetti and G. Prodi. A Primer of Nonlinear Analysis. Cambridge University Press, Cambridge, 1993. 11. S. Antman. Nonlinear Problems of Elasticity. Springer-Verlag, New York- Berlin-Heidelberg, 1995. 12. P. Bachmann. Zahlentheorie. Vierter Teil. Die Arithmetik der quadratischen Formen. Johnson Reprint Corp. 1968, Leipzig, 1898. 13. P. Benevieri and M. Furi. A simple notion of orient ability for Fredholm maps of index zero between Banach manifolds and degree theory. Annales des Sciences Mathematiques du Quebec, 22:131-148, 1998. 14. R. Bohme. Die Losungen der Verzweigungsgleichungen fUr nichtlineare Eigen- wertprobleme. Mathematische Zeitschrijt, 127:105-126, 1970. 15. P. Chossat and G. looss. The Couette-Taylor Problem. Springer-Verlag, New York-Berlin-Heidelberg, 1994. 16. P. Chossat and R. Lauterbach. Methods in Equivariant Bifurcations and Dy- namical Systems. World Scientific Pub!. Co., Singapore, 2000. 17. S.-N. Chow and J.K. Hale. Methods of Bifurcation Theory. Springer-Verlag, New York-Berlin-Heidelberg, 1982.
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References
1. R.A. Adams. Sobolev Spaces. Academic Press, San Diego-London, 1978. 2. S. Agmon. On the eigenfunctions and on the eigenvalues of general elliptic
boundary value problems. Communications on Pure and Applied Mathematics, 15:119-147,1962.
3. J.C. Alexander and J.A. Yorke. Global bifurcation of periodic orbits. American Journal of Mathematics, 100:263-292, 1978.
4. E.L. Allgower and K. Georg. Numerical Continuation Methods. An Introduction. Springer-Verlag, Berlin-Heidelberg-New York, 1990.
5. H. Amann. Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces. SIAM Review, 18:620-709, 1976.
6. H. Amann. Ordinary Differential Equations. de Gruyter, Berlin, 1990. 7. H. Amann. Linear and Quasilinear Parabolic Problems. Volume I: Abstract
Linear Theory. Birkhiiuser, Basel-Boston-Berlin, 1995. 8. H. Amann and S. Weiss. On the uniqueness of the topological degree. Mathe
matische Zeitschrijt, 130:39-54, 1973. 9. A. Ambrosetti. Branching points for a class of variational operators. Journal
d'Analyse Mathematique, 76:321-335, 1998. 10. A. Ambrosetti and G. Prodi. A Primer of Nonlinear Analysis. Cambridge
University Press, Cambridge, 1993. 11. S. Antman. Nonlinear Problems of Elasticity. Springer-Verlag, New York
Berlin-Heidelberg, 1995. 12. P. Bachmann. Zahlentheorie. Vierter Teil. Die Arithmetik der quadratischen
Formen. Johnson Reprint Corp. 1968, Leipzig, 1898. 13. P. Benevieri and M. Furi. A simple notion of orient ability for Fredholm maps of
index zero between Banach manifolds and degree theory. Annales des Sciences Mathematiques du Quebec, 22:131-148, 1998.
14. R. Bohme. Die Losungen der Verzweigungsgleichungen fUr nichtlineare Eigenwertprobleme. Mathematische Zeitschrijt, 127:105-126, 1970.
15. P. Chossat and G. looss. The Couette-Taylor Problem. Springer-Verlag, New York-Berlin-Heidelberg, 1994.
16. P. Chossat and R. Lauterbach. Methods in Equivariant Bifurcations and Dynamical Systems. World Scientific Pub!. Co., Singapore, 2000.
17. S.-N. Chow and J.K. Hale. Methods of Bifurcation Theory. Springer-Verlag, New York-Berlin-Heidelberg, 1982.
336 References
18. S.-N. Chow and R. Lauterbach. A bifurcation theorem for critical points of variational problems. Nonlinear Analysis. Theory, Methods f?j Applications, 12:51-61,1988.
19. S.-N. Chow, J. Mallet-Paret, and J.A. Yorke. Global Hopf bifurcation from a multiple eigenvalue. Nonlinear Analysis. Theory, Methods f?j Applications, 2:753-763,1978.
20. C. Conley. Isolated invariant sets and the Morse index. Regional Conference Series in Mathematics, No. 38. American Mathematical Society, Providence, R.I., 1978.
21. A. Constantin and W. Strauss. Exact periodic traveling water waves with vorticity. Comptes Rendus de l'Academie des Sciences, Paris, Series I, 335:797--800,2002.
22. R. Courant and D. Hilbert. Methods of Mathematical Physics. Interscience, New York, 1953.
23. W. Craig and C.E. Wayne. Newton's method and periodic solutions of nonlinear wave equations. Communications on Pure and Applied Mathematics, 46:1409-1498,1993.
24. M.G. Crandall and P.H. Rabinowitz. Nonlinear Sturm-Liouville eigenvalue problems and topological degree. Journal of Mathematical Mechanics, 19:1083-1102, 1970.
25. M.G. Crandall and P.H. Rabinowitz. Bifurcation from simple eigenvalues. Journal of Functional Analysis, 8:321-340, 1971.
26. M.G. Crandall and P.H. Rabinowitz. Bifurcation, perturbation of simple eigenvalues, and linearized stability. Archive for Rational Mechanics and Analysis, 52: 161-180, 1973.
27. M.G. Crandall and P.H. Rabinowitz. The Hopf Bifurcation Theorem in Infinite Dimensions. Archive for Rational Mechanics and Analysis, 67:53-72, 1977.
28. E.N. Dancer. On the structure of solutions of non-linear eigenvalue problems. Indiana University Mathematics Journal, 23:1069-1076, 1974.
29. E.N. Dancer. Boundary-value problems for ordinary differential equations on infinite intervals. Proceedings of the London Mathematical Society, 30:76--94, 1975.
30. E.N. Dancer. On the number of positive solutions of weakly nonlinear elliptic equations when a parameter is large. Proceedings of the London Mathematical Society, 53:429-452, 1986.
31. E.N. Dancer. The effect of domain shape on the number of positive solutions of certain nonlinear equations II. Journal of Differential Equations, 87:316--339, 1990.
32. K. Deimling. Nonlinear Functional A nalysis. Springer-Verlag, Berlin-New York-Heidelberg, 1985.
33. M. Demazure. Bifurcations and Catastrophes. Geometry of Solutions to Nonlinear Problems. Springer-Verlag, Berlin-Heidelberg-New York, 2000.
34. O. Diekmann, S.A. van Gils, S.M. Verduyn Lunel, and H.-O. Walther. Delay Equations. Springer-Verlag, New York-Berlin-Heidelberg, 1995.
35. J. Dieudonne. Sur Ie polygone de Newton. Archiv der Mathematik, 2:49-55, 1950.
36. J. Dieudonne. Foundations of Modem Analysis. Academic Press, New York, 1964.
37. N. Dunford and J. Schwartz. Linear Operators, Part I: General Theory. WileyInterscience, New York, 1964.
References 337
38. G. Eisenack and C. Fenske. Fixpunkttheorie. Bibliographisches Institut, Mannheim, 1978.
39. K.D. Elworthy and A.J. Tromba. Degree theory on Banach manifolds. Proceedings of Symposia in Pure Mathematics, Volume 18, Part 1. American Mathematical Society, Providence, R.I., pages 86-94, 1970.
40. J. Esquinas. Optimal multiplicity in local bifurcation theory. II: General case. Journal of Differential Equations, 75:206-215, 1988.
41. J. Esquinas and J. Lopez-Gomez. Optimal multiplicity in local bifurcation theory I. Generalized generic eigenvalues. Journal of Differential Equations, 71:72-92, 1988.
42. C. Fenske. Analytische Theorie des Abbildungsgrades fUr Abbildungen in Banachraumen. Mathematische Nachrichten, 48:279-290, 1971.
43. C. Fenske. Extensio gradus ad quasdam applicationes Fredholmii. Mitteilungen aus dem Mathematischen Seminar Giessen, 121:65-70, 1976.
44. B. Fiedler. An index for global Hopf bifurcation in parabolic systems. Journal fur die reine und angewandte Mathematik, 359:1-36, 1985.
45. P.C. Fife, H. Kielh6fer, S. Maier-Paape, and T. Wanner. Perturbation of doubly periodic solution branches with applications to the Cahn-Hilliard equation. Physica D, 100:257-278, 1997.
46. P.M. Fitzpatrick and J. Pejsachowicz. Parity and generalized multiplicity. Transactions of the American Mathematical Society, 326:281-305, 1991.
47. P.M. Fitzpatrick, J. Pejsachowicz, and P.J. Rabier. Orientability of Fredholm Families and Topological Degree for Orientable Nonlinear Fredholm Mappings. Journal of Functional Analysis, 124:1-39, 1994.
48. A. Friedman. Partial Differential Equations. Holt, Rinehart and Winston, New York, 1969.
49. A. Friedman. Partial Differential Equations of Parabolic Type. Robert E. Krieger Pub!. Comp., Malabar, Florida, 1983.
50. R.E. Gaines and J. Mawhin. Coincidence Degree, and Nonlinear Differential Equations. Lectures Notes in Mathematics, Volume 568. Springer-Verlag, Berlin-Heidelberg-New York, 1977.
51. B. Gidas, W.-M. Ni, and L. Nirenberg. Symmetry and related properties via the maximum principle. Communications in Mathematical Physics, 68:209-243, 1979.
52. D. Gilbarg and N.S. Trudinger. Elliptic Partial Differential Equations of Second Order. Springer-Verlag, Berlin-Heidelberg-New York, 1983.
53. M. Golubitsky, J.E. Marsden, I. Stewart, and M. Dellnitz. The Constrained Liapunov-Schmidt Procedure and Periodic Orbits. Fields Institute Communications, 4:81-127, 1995.
54. M. Golubitsky and D.G. Schaeffer. Singularities and Groups in Bifurcation Theory, Volume I. Springer-Verlag, Berlin-Heidelberg-New York, 1985.
55. M. Golubitsky, I. Stewart, and D.G. Schaeffer. Singularities and Groups in Bifurcation Theory, Volume II. Springer-Verlag, Berlin-Heidelberg-New York, 1988.
56. J. Guckenheimer and P. Holmes. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer-Verlag, Berlin-Heidelberg-New York, 1983.
57. C. Gugg, T.J. Healey, H. Kielh6fer, and S. Maier-Paape. Nonlinear Standing and Rotating Waves on the Sphere. Journal of Differential Equations, 166:402-442,2000.
338 References
58. J.K. Hale. Ordinary Differential Equations. John Wiley & Sons, New York, London, Sydney, 1969.
59. J.K. Hale. Theory of Functional Differential Equations. Springer-Verlag, New York-Berlin-Heidelberg, 1977.
60. J.K. Hale and H. Ko<;ak. Dynamics and Bifurcations. Springer-Verlag, New York-Berlin-Heidelberg, 1991.
61. T.J. Healey. Global bifurcation and continuation in the presence of symmetry with an application to solid mechanics. SIAM Journal of Mathematical Analysis, 19:824-840, 1988.
62. T.J. Healey and H. Kielhofer. Symmetry and nodal properties in the global bifurcation analysis of quasi-linear elliptic equations. Archive for Rational Mechanics and Analysis, 113:299-311, 1991.
63. T.J. Healey and H. Kielhofer. Hidden Symmetry of Fully Nonlinear Boundary Conditions in Elliptic Equations: Global Bifurcation and Nodal Structure. Results in Mathematics, 21:83-92, 1992.
64. T.J. Healey and H. Kielhofer. Positivity of global branches of fully nonlinear elliptic boundary value problems. Proceedings of the American Mathematical Society, 115:1031-1036, 1992.
65. T.J. Healey and H. Kielhofer. Preservation of nodal structure on global bifurcating solutions branches of elliptic equations with symmetry. Journal of Differential Equations, 106:70-89, 1993.
66. T.J. Healey and H. Kielhofer. Separation of global solution branches of elliptic systems with symmetry via nodal properties. Nonlinear Analysis. Theory, Methods 8 Applications, 21:665-684, 1993.
67. T.J. Healey and H. Kielhofer. Free nonlinear vibrations for a class of twodimensional plate equations: Standing and discrete-rotating waves. Nonlinear Analysis. Theory, Methods 8 Applications, 29:501-531, 1997.
68. T.J. Healey, H. Kielhofer, and E.L. Montes-Pizarro. Free nonlinear vibrations for plate equations on the equilateral triangle. Nonlinear Analysis. Theory, Methods 8 Applications, 44:575-599, 2001.
69. T.J. Healey, H. Kielhofer, and C.A. Stuart. Global branches of positive weak solutions of semilinear elliptic problems over non-smooth domains. Proceedings of the Royal Society of Edinburgh, 124 A:371-388, 1994.
70. T.J. Healey and H.C. Simpson. Global continuation in nonlinear elasticity. Archive for Rational Mechanics and Analysis, 143:1-28, 1998.
71. D. Henry. Geometric Theory of Semilinear Parabolic Equations. Lecture Notes in Mathematics, Volume 840. Springer-Verlag, Berlin-Heidelberg-New York, 1981.
72. P. Hess and T. Kato. On some linear and nonlinear eigenvalue problems with an indefinite weight function. Communications in Partial Differential Equations, 5:999-1030, 1980.
73. M. Holzmann and H. Kielhofer. Uniqueness of global positive solution branches of nonlinear elliptic problems. Mathematische Annalen, 300:221-241, 1994.
74. E. Hopf. Abzweigung einer periodischen Losung von einer stationaren Losung eines Differentialsystems. Berichte der Siichsischen Akademie der Wis-senschaften, 94:1-22,1942.
75. G. looss and D. Joseph. Elementary Stability and Bifurcation Theory. SpringerVerlag, New York-Berlin-Heidelberg, 1980.
76. J. lze. Bifurcation Theory for Fredholm Operators. Memoirs of the American Mathematical Society 174, Providence, 1976.
References 339
77. J. Ize. Obstruction theory and multiparameter Hopf bifurcation. Tmnsactions of the American Mathematical Society, 289:757-792, 1985.
78. J. Ize. Topological bifurcation. Topological nonlinear analysis: degree, singl1-larity, and variations. Birkhauser-Verlag, Boston, MA, pages 341·-463, 1995.
79. J. Ize, J. Massabo, and A. Vignoli. Degree theory for equivariant maps. 1. Tmnsactions of the American Mathematical Society, 315:4335lO, 1989.
80. T. Kato. Pertl1rbation Theory for Linear Opemtors. Springer-Verlag, BerlinHeidelberg-New York, 1984.
81. H.B. Keller. Nl1merical methods in bifl1rcation problems. Springer-Verlag, Berlin-Heidelberg-New York, 1987.
82. H. Kielhofer. Halbgruppen und semilineare Anfangs-Randwertprobleme. Manl1scT'ipta Mathematica, 12:121-152, 1974.
83. H. KielhOfer. Stability and Semilinear Evolution Equations in Hilbert Space. Archive for Rational Mechanics and Analysis, 57:150-165, 1974.
84. H. Kielhofer. Existenz und Regularitat von Losungen semilinearer parabolischer Anfangs- Randwertprobleme. Mathematische Zeitschrijt, 142:131-160, 1975.
85. H. Kielhofer. On the Lyapunov Stability of Stationary Solutions of Semilinear Parabolic Differential Equations. JOl1rnal of Differential Eql1ations, 22:193-208, 1976.
86. H. Kielhofer. Bifurcation of Periodic Solutions for a Semilinear Wave Equation. JOl1rnal of Mathematical Analysis and Applications, 68:408-420, 1979.
87. H. KielhOfer. Generalized Hopf Bifurcation in Hilbert Space. Mathematical Methods in the Applied Sciences, 1:498-513, 1979.
88. H. Kielhofer. Hopf Bifurcation at Multiple Eigenvalues. Archive for Rational Mechanics and Analysis, 69:53-83, 1979.
89. H. Kielhofer. Degenerate Bifurcation at Simple Eigenvalues and Stability of Bifurcating Solutions. JOl1rnal of Fl1nctional Analysis, 38:416-441, 1980.
90. H. Kielhofer. A Bunch of Stationary or Periodic Solutions Near an Equilibrium by a Slow Exchange of Stability. NonlineaT' Differential Eql1ations: Invanance, Stability, and Bifl1T'cation, Academic Press, New-York, pages 207-219, 1981.
91. H. Kielhofer. Floquet Exponents of Bifurcating Periodic Orbits. NonlineaT' Analysis. Theory, Methods fj Applications, 6:571-583, 1982.
92. H. KielhOfer. Multiple eigenvalue bifurcation for Fredholm operators. JOl1rnal fur die T'eine l1nd angewandte Mathematik, 358:lO4-124, 1985.
93. H. Kielhofer. Interaction of periodic and stationary bifurcation from multiple eigenvalues. Mathematische Zeitschrijt, 192:159-166, 1986.
94. H. Kielhofer. A Bifurcation Theorem for Potential Operators. JOl1rnal of Fl1nctional Analysis, 77:1-8,1988.
95. H. Kielhofer. A Bifurcation Theorem for Potential Operators and an Application to Wave Equations. Proceedings Int. Conf. on Bifl1T'cation Theory and Its Nl1m. Anal. in Xi 'an, China, Xi'an Jiaotong University Press, pages 270 -276, 1989.
96. H. Kielhofer. Hopf Bifurcation from a Differentiable Viewpoint. JOl1rnal of Differential Eq1lations, 97:189-232, 1992.
97. H. Kielhofer. Smoothness and asymptotics of global positive branches of .:111 + )..f(l1) = O. ZAMP. ZeitschrijtfuT' Angewandte Mathematik l1nd Physik, 43:139 153, 1992.
98. H. KielhOfer. Smoothness of global positive branches of nonlinear elliptic problems over symmetric domains. Mathematische Zeitschrift, 211:41-48, 1992.
340 References
99. H. Kielhöfer. Generic Sl-Equivariant Vector Fields. Journal of Dynamics and Differential Equations, 6:277-300, 1994.
100. H. Kielhöfer. Pattern formation of the stationary Cahn-Hilliard model. Proceedings of the Royal Society of Edinburgh, 127 A:1219-1243, 1997.
101. H. Kielhöfer. Minimizing sequences selected via singular perturbations, and their pattern formation. Archive for Rational Mechanics and Analysis, 155:261-276, 2000.
102. H. Kielhöfer. Critical points of nonconvex and noncoercive functionals. Calculus of Variations, 16:243-272, 2003.
103. H. Kielhöfer and P. Kötzner. Stable periods of a semilinear wave equation and bifurcation of periodic solutions. ZAMP. Zeitschrift für Angewandte Mathematik und Physik, 38:204-212, 1987.
104. H. Kielhöfer and R. Lauterbach. On the Principle ofReduced Stability. Journal of Functional Analysis, 53:99-111, 1983.
105. K Kirchgässner. Multiple Eigenvalue Bifurcation for Holomorphic Mappings. Contributions to Nonlinear Functional Analysis. Academic Press, New York, pages 69-99, 1977.
106. K Kirchgässner and H. Kielhöfer. Stability and Bifurcation in Fluid Dynamics. Rocky Mountain Journal of Mathematics, 3:275-318, 1973.
107. K Kirchgässner and J. Scheurle. Verzweigung und Stabilität von Lösungen semilinearer elliptischer Randwertprobleme. Jahresbericht der Deutschen Mathematiker Vereinigung, 77:39-54, 1975.
108. K Kirchgässner and J. Scheurle. Global branches of periodic solutions of reversible systems. Recent Contributions to Nonlinear Partial Differential Equations. Research Notes in Mathematics, 50, Pitman, Boston-LondonMelbourne, pages 103-130, 1981.
109. M.A. Krasnosel'skii. Topological Methods in the Theory of Nonlinear Integral Equations. Pergamon Press, Oxford, 1964.
110. O.A. Ladyzhenskaja, V.A. Solonnikov, and N.N. Ural'ceva. Linear and Quasilinear Equations of Parabolic Type. AMS Transl. Math. Monographs, Vol. 23, Providence, Rhode-Island, 1968.
111. O.A. Ladyzhenskaja and N.N. Ural'ceva. Linear and Quasilinear Elliptic Equati ans. Academic Press, New York-London, 1968.
112. B. Laloux and J. Mawhin. Multiplicity, Leray-Schauder Formula and Bifurcation. Journal of Differential Equations, 24:301-322, 1977.
113. J. Leray and J. Schauder. Topologie et equations fonctionelles. Annales Scientifiques de l'Ecole Normale Superieure, 51:45-78, 1934.
114. J.L. Lions and E. Magenes. Problemes aux limites non homogenes et applications. Non-homogeneous boundary value problems and applications. Dunod, Paris, Springer-Verlag, Berlin-Heidelberg-New York, 1972.
115. P.L. Lions. On the existence of positive solutions of semilinear elliptic equations. SIAM Review, 24:441-467, 1982.
117. J. Lopez-Gomez. Multiparameter Local Bifurcation Based on the Linear Part. Journal of Mathematical Analysis and Applications, 138:358-370, 1989.
118. KW. MacEwen and T.J. Healey. A Simple Approach to the 1:1 Resonance Bifurcation in Follower-Load Problems. Preprint, 2001.
119. R.J. Magnus. A Generalization of Multiplicity and the Problem of Bifurcation. Proceedings of the London Mathematical Society, 32:251-278, 1976.
References 341
120. J. Mallet-Paret and J.A. Yorke. Snakes: Oriented families of periodic orbits, their sourees, sinks, and continuation. Journal 0/ Differential Equations, 43:419-450, 1982.
121. A. Marino. La biforcazione nel caso variazionale. Confer. Sem. Mat. Univ. Bari, 132, Bari, 1973.
122. J. Mawhin. Equivalence theorems for nonlinear operator equations and coincidence degree theory for some mappings in locally convex topological vector spaces. Journal 0/ Differential Equations, 12:610-636, 1972.
123. J. Mawhin. Topological degree methods in nonlinear boundary value problems. Regional conference series in mathematics, Volume 40. American Mathematical Society, Providence, R.L, 1977.
124. J. Mawhin. Nonlinear functional analysis and periodic solutions of semilinear wave equations. Nonlinear phenomena in mathematieal seienees. Academic Press, New York, pages 671-681, 1982.
125. T. Ouyang and J. Shi. Exact multiplicity of positive solutions for a dass of semilinear problems. 11. Journal 0/ Differential Equations, 158:94-151, 1999.
126. A. Pazy. SemigTOups 0/ Linear Operators and Applications to Partial Differential Equations. Springer-Verlag, New York-Berlin-Heidelberg, 1983.
127. H.O. Peitgen and K. Schmitt. Global topological perturbations of nonlinear elliptic eigenvalue problems. Mathematieal Methods in the Applied Seienees, 5:376-388, 1983.
128. G.H. Pimbley. Eigen/unction Branehes 0/ Nonlinear Operators, and Their Bi/ureations. Lecture Notes in Mathematics, Volume 104. Springer-Verlag, Berlin-Heidelberg-New York, 1969.
129. F. Quinn and A. Sard. Hausdorff conullity of critical images of Fredholm maps. American Journal 0/ Mathematics, 94:1101-1110, 1972.
130. P.J. Rabier. Generalized Jordan chains and two bifurcation theorems of Krasnoselskii. Nonlinear Analysis. Theory, Methods &J Applications, 13:903-934, 1989.
131. P.H. Rabinowitz. Some global results for nonlinear eigenvalue problems. Journal 0/ Functional Analysis, 7:487-513, 1971.
132. P.H. Rabinowitz. Time periodic solutions of nonlinear wave equations. Manuseripta Mathematiea, 5:165-194, 1971.
133. P.H. Rabinowitz. On Bifurcation From Infinity. Journal 0/ Differential Equations, 14:462-475, 1973.
134. P.H. Rabinowitz. Variational methods for nonlinear eigenvalue problems. C.I.M.E. III. Ciclo, Varenna, 1974, Edizione Cremonese, Roma, pages 139-195, 1974.
135. P.H. Rabinowitz. A Bifurcation Theorem for Potential Operators. Journal 0/ Functional Analysis, 25:412-424, 1977.
136. P.H. Rabinowitz. Free vibrations for a semilinear wave equation. Communieations on Pure and Applied Mathematies, 31:31-68, 1978.
137. P. Sarreither. Transformationseigenschaften endlicher Ketten und allgemeine Verzweigungsaussagen. Mathematiea Scandinavica, 35:115-128, 1974.
138. D.H. Sattinger. Topies in Stability and Bi/urcation Theory. Lecture Notes in Mathematics, Volume 309. Springer-Verlag, Berlin-Heidelberg-New York, 1972.
139. R. Schaaf. Global Solution Branehes 0/ Two Point Boundary Value Problems. Lecture Notes in Mathematics, Volume 1458. Springer-Verlag, BerlinHeidelberg-New York, 1990.
342 References
140. D. S. Schmidt. Hopf's bifurcation theorem and the center theorem of Liapunov. Celestical Mechanics, 9:81-103, 1976.
141. M. Sevryuk. Reversible systems. Lecture Notes in Mathematics, Volume 1211. Springer-Verlag, Berlin-Heidelberg-New York, 1986.
142. R. Seydel. Practical bi/urcation and stability analysis: /rom equilibrium to chaos. 2nd ed. Springer-Verlag, New York, 1994.
143. S. Smale. An Infinite Dimensional Version of Sard's Theorem. American Journal 0/ Mathematics, 87:861-866, 1965.
144. J.A. Smoller and A.G. Wasserman. Existence, uniqueness, and nondegeneracy of positive solutions of semilinear elliptic equations. Communications in Mathematical Physics, 95:129-159, 1984.
145. P.E. Sobolevskii. Equations of Parabolic Type in Banach Space. American Mathematical Society, Translation Series II, 49:1-62, 1966.
146. A. Vanderbauwhede. Local bi/urcation and symmetry. Research Notes in Mathematics, 75. Pitman, Boston-London-Melbourne, 1982.
147. A. Vanderbauwhede. Hopf bifurcation for equivariant conservative and timereversible systems. Proceedings 0/ the Royal Society 0/ Edinburgh, 116 A:103-128, 1990.
148. W. von Wahl. Gebrochene Potenzen eines elliptischen Operators und parabolische Differentialgleichungen in Räumen hölderstetiger Funktionen. Nachrichten der Akademie der Wissenschaften Göttingen, JI. Math. Physik. Klasse, 11:231-258, 1972.
149. H.F. Weinberger. On the stability of bifurcating solutions. Nonlinear Analysis. A Collection 0/ Papers in Honor 0/ Erich Rothe. Academic Press, New York, pages 219-233, 1978.
150. D. Westreich. Bifurcation at eigenvalues of odd multiplicity. Proceedings 0/ the American Mathematical Society, 41:609-614, 1973.
151. G. T. Whyburn. Topological Analysis. Princeton University Press, New Jersey, 1958.
152. K. Yosida. Functional Analysis. Springer-Verlag, Berlin-Heidelberg-New York, 1980.
153. E. Zeidler. Nonlinear Functional Analysis and its Applications. I: Fixed-Point Theorems. Springer-Verlag, New York-Berlin-Heidelberg, 1986.
Global Bifurcation Theorem for Fredholm Operators, 206
Global Bifurcation with One-Dimensional KerneI, 206
global branch, 283 global continuation, 211, 281, 283, 300 Global Implicit Function Theorem, 210 global parameterization, 320 Global Positive Solution Branches, 284,
290, 300, 302
Hamiltonian Hopf Bifurcation, 61, 66 Hamiltonian Hopf Bifurcation for
Reversible Systems, 68 Hamiltonian Hopf Bifurcation for
Conservative Systems, 74 Hamiltonian Hopf Bifurcation for