Some results on solutions of minimal period to superquadratic Hamiltonian systems

DOI10.1016/0362-546X(83)90039-1zbMath0512.70021MaRDI QIDQ3657496

Mario Girardi, Michele Matzeu

Publication date: 1983

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

zbMATH Keywords

prescribed minimal periodsuperquadratic Hamiltonian systemshomogeneous of degree betaminimum positive critical value

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Hamilton's equations (70H05) Hamilton's principle (70H25)

Related Items (25)

Periodic solutions with prescribed minimal period for convex autonomous Hamiltonian systems ⋮ Generalized Ambrosetti-Rabinowitz condition for minimal period solutions of autonomous Hamiltonian systems ⋮ Unnamed Item ⋮ Periodic solutions of convex autonomous Hamiltonian systems with a quadratic growth at the origin and superquadratic at infinity ⋮ Retracted article: ``Minimal period symmetric solutions for some Hamiltonian systems via the Nehari manifold method ⋮ Solutions of minimal period for a class of nonconvex Hamiltonian systems and applications to the fixed energy problem ⋮ Multiple periodic solutions for \(\Gamma\)-symmetric Newtonian systems ⋮ The minimal period problem for nonconvex even second order Hamiltonian systems ⋮ Periodic solutions for a class of symmetric and subquadratic Hamiltonian systems ⋮ Ground state periodic solutions of second order Hamiltonian systems without spectrum 0 ⋮ Orbits with minimal period for a class of autonomous second order one-dimensional Hamiltonian systems ⋮ The iteration formula of the Maslov-type index theory with applications to nonlinear Hamiltonian systems ⋮ A note on the minimal periodic solutions of nonconvex superlinear Hamiltonian system ⋮ Multiple periodic solutions for damped vibration systems with general nonlinearities at infinity ⋮ Symmetric period solutions with prescribed minimal period for even autonomous semipositive Hamiltonian systems ⋮ Minimal period problems for brake orbits of nonlinear autonomous reversible semipositive Hamiltonian systems ⋮ Multiple minimal periodic solutions for subquadratic second-order Hamiltonian systems ⋮ Periodic solutions for Hamiltonian systems without Ambrosetti-Rabinowitz condition and spectrum 0 ⋮ On the minimal periodic solutions of nonconvex superlinear Hamiltonian systems ⋮ Periodic solutions with prescribed minimal period for second order even Hamiltonian systems ⋮ Minimal period estimates of periodic solutions for superquadratic Hamiltonian systems ⋮ Solutions of minimal period for even classical Hamiltonian systems ⋮ On the existence of minimal periodic solutions for a class of second-order Hamiltonian systems ⋮ The Rabinowitz minimal periodic solution conjecture ⋮ The minimal period problem of classical Hamiltonian systems with even potentials

Cites Work

• Periodic solutions of Hamiltonian equations and a theorem of P. Rabinowitz
• On the number of periodic trajectories for a Hamiltonian flow on a convex energy surface
• Solutions of minimal period for a class of convex Hamiltonian systems
• On subharmonic solutions of hamiltonian systems
• Periodic solutions of hamiltonian systems
• Hamiltonian trajectories having prescribed minimal period

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