Periodic solutions of convex autonomous Hamiltonian systems with a quadratic growth at the origin and superquadratic at infinity

DOI10.1007/BF01762410zbMath0631.58014OpenAlexW2023274193MaRDI QIDQ1094715

Mario Girardi, Michele Matzeu

Publication date: 1987

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01762410

zbMATH Keywords

periodic solutionscritical pointsHamiltonian systemprescribed minimal period

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)

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Cites Work

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• Une théorie de Morse pour les systèmes hamiltoniens convexes
• Symmetry breaking in Hamiltonian systems
• Periodic solutions of Hamiltonian equations and a theorem of P. Rabinowitz
• Periodic solutions to Hamiltonian inclusions
• Solutions of minimal period for a class of convex Hamiltonian systems
• Closed orbits of fixed energy for a class of \(N\)-body problems
• Dual variational methods in critical point theory and applications
• Lusternik-Schnirelman theory on Banach manifolds
• On differentiable functions with isolated critical points
• Survey of works on conditions of stability of the trivial solution of a system of linear differential equations with periodic coefficients
• Some results on solutions of minimal period to superquadratic Hamiltonian systems
• Existence of multiple periodic orbits on star‐shaped hamiltonian surfaces
• A Geometric Description of the Neighbourhood of a Critical Point Given by the Mountain-Pass Theorem
• Periodic Solutions of Hamilton's Equations and Local Minima of the Dual Action
• Solutions of minimal period for a class of nonconvex Hamiltonian systems and applications to the fixed energy problem
• On subharmonic solutions of hamiltonian systems
• Periodic solutions of hamiltonian systems
• Hamiltonian trajectories having prescribed minimal period
• Morse‐type index theory for flows and periodic solutions for Hamiltonian Equations
• Periodic solutions of asymptotically linear Hamiltonian systems