Morse theory and existence of periodic solutions of convex hamiltonian systems
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Publication:3822869
DOI10.24033/bsmf.2094zbMath0669.58004OpenAlexW2232102173MaRDI QIDQ3822869
Publication date: 1988
Published in: Bulletin de la Société mathématique de France (Search for Journal in Brave)
Full work available at URL: http://www.numdam.org/item?id=BSMF_1988__116_2_171_0
Periodic solutions to ordinary differential equations (34C25) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05)
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Cites Work
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- Morse theory on Branach space and its applications to partial differential equations
- Une théorie de Morse pour les systèmes hamiltoniens convexes
- Periodic solutions with prescribed minimal period for convex autonomous Hamiltonian systems
- Multiplicité des trajectoires fermées de systèmes hamiltoniens connexes. (Multiplicity of closed trajectories of convex Hamiltonian systems)
- Critical point theory and the number of solutions of a nonlinear Dirichlet problem
- On the number of periodic trajectories for a Hamiltonian flow on a convex energy surface
- On saddle point problems in the calculus of variations, the Rity algorithm, and monotone convergence
- Morse theory in Hilbert space
- On differentiable functions with isolated critical points
- Inequalities of critical point theory
- Periodic Solutions of Hamiltonian Systems: A Survey
- Existence of multiple periodic orbits on star‐shaped hamiltonian surfaces
- Nonconvex minimization problems
- Hamiltonian trajectories having prescribed minimal period