Multiplicity of subharmonic solutions of forced Hamiltonian systems near an equilibrium

1989 ◽  
Vol 64 (4) ◽  
pp. 389-402 ◽  
Author(s):  
Maria Letizia Bertotti
Keyword(s):  
Hamiltonian Systems ◽  
Subharmonic Solutions

scholarly journals Subharmonic solutions of bounded coupled Hamiltonian systems with sublinear growth

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Fanfan Chen ◽  
Dingbian Qian ◽  
Xiying Sun ◽  
Yinyin Wu
Keyword(s):  
Hamiltonian Systems ◽  
Phase Plane ◽  
Phase Plane Analysis ◽  
Zero Eigenvalue ◽  
Subharmonic Solutions ◽  
Existence And Multiplicity ◽  
Plane Analysis ◽  
Higher Dimensional ◽  
Dimensional Version ◽  
Twist Theorem

<p style='text-indent:20px;'>We prove the existence and multiplicity of subharmonic solutions for bounded coupled Hamiltonian systems. The nonlinearities are assumed to satisfy Landesman-Lazer conditions at the zero eigenvalue, and to have some kind of sublinear behavior at infinity. The proof is based on phase plane analysis and a higher dimensional version of the Poincaré-Birkhoff twist theorem by Fonda and Ureña. The results obtained generalize the previous works for scalar second-order differential equations or relativistic equations to higher dimensional systems.</p>

One-Signed Harmonic Solutions and Sign-Changing Subharmonic Solutions to Scalar Second Order Differential Equations

2012 ◽  
Vol 12 (3) ◽  
Author(s):  
Alberto Boscaggin
Keyword(s):  
Fixed Point ◽  
Continuous Function ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Hamiltonian Systems ◽  
Point Theorem ◽  
Second Order ◽  
Second Order Differential Equations ◽  
Subharmonic Solutions

AbstractUsing a recent modified version of the Poincaré-Birkhoff fixed point theorem [19], we study the existence of one-signed T-periodic solutions and sign-changing subharmonic solutions to the second order scalar ODEu′′ + f (t, u) = 0,being f : ℝ × ℝ → ℝ a continuous function T-periodic in the first variable and such that f (t, 0) ≡ 0. Partial extensions of the results to a general planar Hamiltonian systems are given, as well.

Subharmonic Solutions of Planar Hamiltonian Systems: a Rotation Number Approach

2011 ◽  
Vol 11 (1) ◽  
Author(s):  
Alberto Boscaggin
Keyword(s):  
Hamiltonian System ◽  
Hamiltonian Systems ◽  
Rotation Number ◽  
Subharmonic Solutions ◽  
Planar Hamiltonian System ◽  
Nodal Properties

AbstractWe prove the existence of infinitely many subharmonic solutions, with prescribed nodal properties, for a planar Hamiltonian system Jz′ = Δ

scholarly journals Subharmonic solutions of Hamiltonian systems displaying some kind of sublinear growth

2017 ◽  
Vol 8 (1) ◽  
pp. 583-602 ◽  
Author(s):  
Alessandro Fonda ◽  
Rodica Toader
Keyword(s):  
Hamiltonian Systems ◽  
Zero Eigenvalue ◽  
Birkhoff Theorem ◽  
Subharmonic Solutions ◽  
Existence And Multiplicity ◽  
Volterra Systems

Abstract We prove the existence and multiplicity of subharmonic solutions for Hamiltonian systems obtained as perturbations of N planar uncoupled systems which, e.g., model some type of asymmetric oscillators. The nonlinearities are assumed to satisfy Landesman–Lazer conditions at the zero eigenvalue, and to have some kind of sublinear behavior at infinity. The proof is carried out by the use of a generalized version of the Poincaré–Birkhoff Theorem. Different situations, including Lotka–Volterra systems, or systems with singularities, are also illustrated.

Periodic and subharmonic solutions for a class of non-autonomous Hamiltonian systems

2012 ◽  
Vol 75 (4) ◽  
pp. 2262-2272 ◽  
Author(s):  
Chun Li ◽  
Zeng-Qi Ou ◽  
Chun-Lei Tang
Keyword(s):  
Hamiltonian Systems ◽  
Subharmonic Solutions
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