An avoiding cones condition for the Poincaré-Birkhoff theorem

DOI10.1016/j.jde.2016.10.002zbMath1369.37064OpenAlexW2536708615MaRDI QIDQ340357

Alessandro Fonda, Paolo Gidoni

Publication date: 14 November 2016

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2016.10.002

zbMATH Keywords

periodic solutionsHamiltonian systemsavoiding cones conditionPoincaré-Birkhoff theorem

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25)

Related Items (8)

Lower bound on the number of periodic solutions for asymptotically linear planar Hamiltonian systems ⋮ Periodic solutions of Hamiltonian systems coupling twist with generalized lower/upper solutions ⋮ An extension of the Poincaré-Birkhoff theorem coupling twist with lower and upper solutions ⋮ Coupling linearity and twist: an extension of the Poincaré-Birkhoff theorem for Hamiltonian systems ⋮ A new fixed point theorem and periodic solutions of nonconservative weakly coupled systems ⋮ Multiplicity of periodic solutions for systems of weakly coupled parametrized second order differential equations ⋮ Subharmonic solutions of bounded coupled Hamiltonian systems with sublinear growth ⋮ Periodic solutions of superlinear and sublinear state-dependent discontinuous differential equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Periodic perturbations of Hamiltonian systems
• Multiple periodic solutions of Hamiltonian systems confined in a box
• Generalizing the Poincaré-Miranda theorem: the avoiding cones condition
• Periodic solutions of weakly coupled superlinear systems
• The Birkhoff-Lewis fixed point theorem and a conjecture of V.I. Arnold
• Periodic solutions of spatially periodic Hamiltonian systems
• A higher-dimensional Poincaré-Birkhoff theorem without monotone twist
• Cohomology and Morse theory for strongly indefinite functionals
• A generalized saddle point theorem
• Periodic solutions of perturbed Hamiltonian systems in the plane by the use of the Poincaré-Birkhoff theorem
• On the periodic nonlinearity and the multiplicity of solutions
• A relative category and applications to critical point theory for strongly indefinite functionals

This page was built for publication: An avoiding cones condition for the Poincaré-Birkhoff theorem