Iteration inequalities of the Maslov \(P\)-index theory with applications

DOI10.1016/j.na.2015.06.029zbMath1358.37104OpenAlexW1409688781MaRDI QIDQ499627

Shanshan Tang, Chun-gen Liu

Publication date: 30 September 2015

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2015.06.029

zbMATH Keywords

Hamiltonian systems\(P\)-symmetric periodic solutioniteration inequalityMaslov \(P\)-indexminimal period problem

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Lagrangian submanifolds; Maslov index (53D12)

Related Items

Minimal \(P\)-symmetric period problem of first-order autonomous Hamiltonian systems, Minimal \(\mathcal{M} \)-symmetric periodic solutions of general Hamiltonian systems and delay differential equations, Subharmonic \(P^{l}\)-solutions of first order Hamiltonian systems, Minimal \(P\)-cyclic periodic brake orbits in Hamiltonian systems, Subharmonic solutions and minimal periodic solutions of first-order variant subquadratic Hamiltonian systems, The existence of periodic solutions for second-order delay differential systems, A note on the relations between the various index theories, Subharmonic solutions and minimal periodic solutions of first-order Hamiltonian systems with anisotropic growth, Elliptic and non-hyperbolic closed characteristics on compact convex P-cyclic symmetric hypersurfaces in \(\mathbb{R}^{2n} \), Minimal period estimates on \(P\)-symmetric periodic solutions of first-order mild superquadratic Hamiltonian systems

Cites Work

• Unnamed Item
• Forced vibrations of superquadratic Hamiltonian systems
• Hyperbolic closed characteristics on compact convex smooth hypersurfaces in \(\mathbb{R}^{2n}\)
• Bott formula of the Maslov-type index theory
• Minimal period estimates of periodic solutions for superquadratic Hamiltonian systems
• Closed characteristics on partially symmetric compact convex hypersurfaces in \(\mathbb R^{2n}\).
• Subharmonic solutions of Hamiltonian systems
• Iteration inequalities of the Maslov-type index theory with applications
• Closed characteristics on compact convex hypersurfaces in \(\mathbb{R}^{2n}\)
• Morse index estimates in min-max theorems
• Index theory for symplectic paths with applications
• Hyperbolic characteristics on star-shaped hypersurfaces
• Maslov \(P\)-index theory for a symplectic path with applications
• Closed characteristics on non-degenerate star-shaped hypersurfaces in \(\mathbb R^{2n}\)
• Maslov (P, ω)-Index Theory for Symplectic Paths
• 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.
• Periodic solutions of hamiltonian systems
• The iteration formula of the Maslov-type index theory with applications to nonlinear Hamiltonian systems
• P-index theory for linear Hamiltonian systems and multiple solutions for nonlinear Hamiltonian systems