Analytic Hamiltonian Systems, the Vicinity of a Periodic Solution

1995 ◽  
pp. 471-484
Author(s):  
C. Marchal ◽  
J. P. Issartel
Keyword(s):  
Periodic Solution ◽  
Hamiltonian Systems

scholarly journals Variational Approach to Quasi-Periodic Solution of Nonautonomous Second-Order Hamiltonian Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Juhong Kuang
Keyword(s):  
Periodic Solution ◽  
Variational Methods ◽  
Periodic Solutions ◽  
Hamiltonian Systems ◽  
Variational Approach ◽  
Second Order ◽  
New Approach ◽  
Second Order Hamiltonian Systems

We deal with the quasi-periodic solutions of the following second-order Hamiltonian systemsx¨(t)=∇F(t,x(t)), wherex(t)=(x1(t),…,xN(t)), and we present a new approach via variational methods and Minmax method to obtain the existence of quasi-periodic solutions to the above equation.

scholarly journals Periodic Solutions for Second Order Hamiltonian Systems with Impulses via the Local Linking Theorem

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Longsheng Bao ◽  
Binxiang Dai
Keyword(s):  
Periodic Solution ◽  
Hamiltonian System ◽  
Periodic Solutions ◽  
Hamiltonian Systems ◽  
Second Order ◽  
Linking Theorem ◽  
Local Linking ◽  
Second Order Hamiltonian Systems ◽  
New Criterion

A class of second order impulsive Hamiltonian systems are considered. By applying a local linking theorem, we establish the new criterion to guarantee that this impulsive Hamiltonian system has at least one nontrivial T-periodic solution under local superquadratic condition. This result generalizes and improves some existing results in the known literature.

Orbits with minimal period for a class of autonomous second order one-dimensional Hamiltonian systems

2018 ◽  
Vol 25 (1) ◽  
pp. 117-122 ◽  
Author(s):  
Chouhaïd Souissi
Keyword(s):  
Periodic Solution ◽  
Hamiltonian System ◽  
Variational Method ◽  
Hamiltonian Systems ◽  
Second Order ◽  
Minimal Period ◽  
One Dimensional ◽  
Order Hamiltonian System ◽  
Second Order Hamiltonian System

AbstractWe show, under an iterative condition which is similar to but stronger than that of Ambrosetti and Rabinowitz and by using a variational method, the existence of aT-periodic solution of the autonomous superquadratic second order Hamiltonian system with even potential\ddot{z}+V^{\prime}(z)=0,\quad z\in\mathbb{R},for any{T>0}. Moreover, such a solution has{T/k}as a minimal period for some integer{1\leq k\leq 3}.

Sign in / Sign up

Export Citation Format

Share Document