Multiple periodic solutions for one-sided sublinear systems: a refinement of the Poincaré-Birkhoff approach

DOI10.12775/TMNA.2019.104zbMath1472.34076arXiv1901.09406MaRDI QIDQ2194625

Fabio Zanolin, Tobia Dondè

Publication date: 4 September 2020

Published in: Topological Methods in Nonlinear Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.09406

zbMATH Keywords

periodic solutionsPoincaré-Birkhoff theoremcomplex oscillations.topological horse-shoes

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Applications of operator theory to differential and integral equations (47N20) Complex behavior and chaotic systems of ordinary differential equations (34C28) Topological dynamics of nonautonomous systems (37B55) Nonautonomous smooth dynamical systems (37C60)

Related Items (6)

Periodic solutions to superlinear indefinite planar systems: a topological degree approach ⋮ Subharmonic solutions for a class of predator-prey models with degenerate weights in periodic environments ⋮ Multiple Periodic Solutions for a Duffing Type Equation with One-Sided Sublinear Nonlinearity: Beyond the Poincaré-Birkhoff Twist Theorem ⋮ The Poincaré-Birkhoff theorem for a class of degenerate planar Hamiltonian systems ⋮ On the applicability of the Poincaré-Birkhoff twist theorem to a class of planar periodic predator-prey models ⋮ High multiplicity and chaos for an indefinite problem arising from genetic models

Cites Work

• A higher dimensional Poincaré-Birkhoff theorem for Hamiltonian flows
• Periodic solutions of Duffing's equations with superquadratic potential
• Maslov index, Poincaré-Birkhoff theorem and periodic solutions of asymptotically linear planar Hamiltonian systems
• On the continuation of solutions of a certain non-linear differential equation
• Subharmonic Solutions of Planar Hamiltonian Systems: a Rotation Number Approach
• On the Periodic Boundary Value Problem and Chaotic-like Dynamics for Nonlinear Hill’s Equations
• Minimization Problems for Noncoercive Functionals Subject to Constraints
• Sign-Changing Subharmonic Solutions to Unforced Equations with Singular ϕ-Laplacian
• On Continuability of Solutions of Second Order Differential Equations

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