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.

scholarly journals Periodic Solutions of Some Impulsive Hamiltonian Systems with Convexity Potentials

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Dezhu Chen ◽  
Binxiang Dai
Keyword(s):  
Variational Methods ◽  
Periodic Solutions ◽  
Hamiltonian Systems ◽  
Existence Theorems ◽  
Second Order ◽  
Second Order Hamiltonian Systems ◽  
Existence Of Periodic Solutions

We study the existence of periodic solutions of some second-order Hamiltonian systems with impulses. We obtain some new existence theorems by variational methods.

Sign in / Sign up

Export Citation Format

Share Document