Symmetric period solutions with prescribed minimal period for even autonomous semipositive Hamiltonian systems

DOI10.1007/S11425-013-4598-9zbMath1334.37073OpenAlexW2008067969MaRDI QIDQ476634

Duanzhi Zhang

Publication date: 2 December 2014

Published in: Science China. Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11425-013-4598-9

zbMATH Keywords

Maslov-type indexminimal periodeven Hamiltonian systemssemipositivesymmetric periodic solution

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Hamilton's equations (70H05) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05)

Related Items (15)

Generalized Ambrosetti-Rabinowitz condition for minimal period solutions of autonomous Hamiltonian systems ⋮ Minimal brake orbits of first-order convex Hamiltonian systems with anisotropic growth ⋮ Minimal periodic solutions of first-order convex Hamiltonian systems with anisotropic growth ⋮ Some progress on minimal period problems in reversible semi-positive Hamiltonian systems ⋮ Minimal \(P\)-cyclic periodic brake orbits in Hamiltonian systems ⋮ Multiple subharmonic solutions in Hamiltonian system with symmetries ⋮ Subharmonic solutions and minimal periodic solutions of first-order variant subquadratic 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 ⋮ Subharmonic solutions and minimal periodic solutions of first-order Hamiltonian systems with anisotropic growth ⋮ Minimal period solutions in asymptotically linear Hamiltonian system with symmetries ⋮ Periodic solutions with prescribed minimal period for second order even Hamiltonian systems ⋮ Minimal period problem for second-order Hamiltonian systems with asymptotically linear nonlinearities ⋮ On the existence of minimal periodic solutions for a class of second-order Hamiltonian systems ⋮ The Rabinowitz minimal periodic solution conjecture

Cites Work

• Unnamed Item
• Unnamed Item
• Periodic solutions with prescribed minimal period for convex autonomous Hamiltonian systems
• Solutions with minimal period for Hamiltonian systems in a potential well
• Periodic solutions of convex autonomous Hamiltonian systems with a quadratic growth at the origin and superquadratic at infinity
• Solutions of minimal period for a class of convex Hamiltonian systems
• Bott formula of the Maslov-type index theory
• Minimal period estimates of periodic solutions for superquadratic Hamiltonian systems
• The minimal period problem of classical Hamiltonian systems with even potentials
• The minimal period problem of periodic solutions for autonomous superquadratic second order Hamiltonian systems
• Nontrivial periodic solutions for strong resonance Hamiltonian systems
• On the minimal period for the periodic solutions problem of nonlinear Hamiltonian systems
• Iteration inequalities of the Maslov-type index theory with applications
• Solutions of minimal period for even classical Hamiltonian systems
• Cohomology and Morse theory for strongly indefinite functionals
• Morse index estimates in min-max theorems
• Index theory for symplectic paths with applications
• \(P\)-cyclic symmetric closed characteristics on compact convex \(P\)-cyclic symmetric hypersurface in \(\mathbb{R}^{2n}\)
• Periodic solutions with prescribed minimal period for the second order Hamiltonian systems with even potentials
• Maslov-type index theory for symplectic paths and spectral flow. I
• Multiple brake orbits in bounded convex symmetric domains
• A note on the monotonicity of the Maslov-type index of linear Hamiltonian systems with applications
• Some results on solutions of minimal period to superquadratic Hamiltonian systems
• Solutions of minimal period for a class of nonconvex Hamiltonian systems and applications to the fixed energy problem
• Nontrivial solutions of operator equations and Morse indices of critical points of min-max type
• Location, multiplicity and Morse indices of min-max critical points.
• Dual Morse index estimates for periodic solutions of Hamiltonian systems in some nonconvex superquadratic cases
• Periodic solutions of hamiltonian systems
• On the index theories for second order Hamiltonian systems
• On the maslov index
• The iteration formula of the Maslov-type index theory with applications to nonlinear Hamiltonian systems
• Minimal period solutions of nonlinear hamiltonian systems
• Periodic solutions of asymptotically linear Hamiltonian systems

This page was built for publication: Symmetric period solutions with prescribed minimal period for even autonomous semipositive Hamiltonian systems