scholarly journals Subharmonic solutions and minimal periodic solutions of first-order Hamiltonian systems with anisotropic growth

2017 ◽  
Vol 37 (3) ◽  
pp. 1559-1574 ◽  
Author(s):  
Chungen Liu ◽  
◽  
Xiaofei Zhang
Keyword(s):  
Periodic Solutions ◽  
Hamiltonian Systems ◽  
Anisotropic Growth ◽  
First Order ◽  
Subharmonic Solutions

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.

scholarly journals Symmetric periodic solutions of symmetric Hamiltonians in 1:1 resonance

2020 ◽  
Author(s):  
Yocelyn Pérez ◽  
Claudio Vidal
Keyword(s):  
Periodic Solutions ◽  
Hamiltonian Systems ◽  
Analytical Approach ◽  
Hamiltonian Function ◽  
First Order ◽  
The Family ◽  
The Stability

The aim of this work is to prove analytically the existence of symmetric periodic solutions of the family of Hamiltonian systems with Hamiltonian function H(q_1,q_2,p_1,p_2)= 1/2(q_1^2+p_1^2)+1/2(q_2^2+p_2^2)+ a q_1^4+b q_1^2q_2^2+c \q_2^4 with three real parameters a, b and c. Moreover, we characterize the stability of these periodic solutions as function of the parameters. Also, we find a first-order analytical approach of these symmetric periodic solutions. We emphasize that these families of periodic solutions are different from those that exist in the literature.

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