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On critical point theory for indefinite functionals in the presence of symmetries. (English) Zbl 0504.58014


MSC:

58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
22E70 Applications of Lie groups to the sciences; explicit representations
34C25 Periodic solutions to ordinary differential equations
37C80 Symmetries, equivariant dynamical systems (MSC2010)
70H05 Hamilton’s equations
37G99 Local and nonlocal bifurcation theory for dynamical systems

Citations:

Zbl 0465.49006
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References:

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[2] Herbert Amann and Eduard Zehnder, Periodic solutions of asymptotically linear Hamiltonian systems, Manuscripta Math. 32 (1980), no. 1-2, 149 – 189. · Zbl 0443.70019 · doi:10.1007/BF01298187
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[7] Vieri Benci and Paul H. Rabinowitz, Critical point theorems for indefinite functionals, Invent. Math. 52 (1979), no. 3, 241 – 273. · Zbl 0465.49006 · doi:10.1007/BF01389883
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[9] Ivar Ekeland and Jean-Michel Lasry, Sur le nombre de points critiques de fonctions invariantes par des groupes, C. R. Acad. Sci. Paris Sér. A-B 282 (1976), no. 11, Ai, A559 – A562 (French, with English summary). · Zbl 0343.46035
[10] Edward R. Fadell and Paul H. Rabinowitz, Generalized cohomological index theories for Lie group actions with an application to bifurcation questions for Hamiltonian systems, Invent. Math. 45 (1978), no. 2, 139 – 174. · Zbl 0403.57001 · doi:10.1007/BF01390270
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[14] Paul H. Rabinowitz, On subharmonic solutions of Hamiltonian systems, Comm. Pure Appl. Math. 33 (1980), no. 5, 609 – 633. · Zbl 0425.34024 · doi:10.1002/cpa.3160330504
[15] -, Periodic solutions of Hamiltonian systems, Comm. Pure Appl. Math. 31 (1978), 225-251.
[16] -, Variational methods for finding periodic solutions of differential equations, Nonlinear Evolution Equations (M. Crandall, editor), Academic Press, New York, 1978, pp. 225-251.
[17] Martin Schechter, Spectra of partial differential operators, 2nd ed., North-Holland Series in Applied Mathematics and Mechanics, vol. 14, North-Holland Publishing Co., Amsterdam, 1986. · Zbl 0607.35005
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