Subharmonic Solutions of Planar Hamiltonian Systems: a Rotation Number Approach-Reference-Cited by-同舟云学术

Subharmonic Solutions of Planar Hamiltonian Systems: a Rotation Number Approach

Published:2011-02-01 Issue:1 Volume:11 Page:77-103
ISSN:2169-0375
Container-title:Advanced Nonlinear Studies
language:en
Short-container-title:

Author:

Boscaggin Alberto¹

Affiliation:

1. SISSA - ISAS, International School for Advanced Studies via Bonomea 265, 34136 Trieste, Italy

Abstract

Abstract We prove the existence of infinitely many subharmonic solutions, with prescribed nodal properties, for a planar Hamiltonian system Jz′ = ΔzH(t, z), with H periodic in the first variable. The goal is achieved by performing estimates of the rotation numbers with respect to deformed polar coordinates and applying Ding’s version of the Poincaré-Birkhoff fixed point theorem.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics,Statistical and Nonlinear Physics

Link

https://www.degruyter.com/document/doi/10.1515/ans-2011-0104/pdf

Reference11 articles.

1. A note on uniqueness of Cauchy problems associated to planar Hamiltonian systems Portu - gal;Rebelo;Math,2000

2. Subharmonic solutions of second order nonlinear equations : a time - map ap - proach Nonlinear Subharmonic solutions of planar Hamiltonian systems Landesman - Lazer conditions for periodic boundary value problems with asymmetric nonlin - earities;Ding;Anal Differential Equations,1993

3. Maslov index Poincare - Birkhoff theorem and periodic solutions of asymptotically linear planar Hamiltonian systems;Margheri;Differential Equations,2002

4. On second order periodic symmetric differential systems having subharmon - ics of all sufficiently large orders;Cac;Differential Equations,1996

5. Subharmonic solutions for some second - order differential equations with singularities Siam;Fonda;Math Anal,1993

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