scholarly journals New Periodic Solutions for the Singular Hamiltonian System

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
Yi Liao
Keyword(s):  
Hamiltonian System ◽  
Periodic Solutions ◽  
Hamiltonian Systems ◽  
Second Order ◽  
Singular Case ◽  
Strong Force ◽  
Second Order Hamiltonian Systems ◽  
Palais Smale Condition ◽  
Singular Hamiltonian System ◽  
Force Potential

By use of the Cerami-Palais-Smale condition, we generalize the classical Weierstrass minimizing theorem to the singular case by allowing functions which attain infinity at some values. As an application, we study certain singular second-order Hamiltonian systems with strong force potential at the origin and show the existence of new periodic solutions with fixed periods.

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.

Homoclinic orbits for a class of singular second order Hamiltonian systems in ℝ3

2012 ◽  
Vol 10 (6) ◽  
Author(s):  
Joanna Janczewska ◽  
Jakub Maksymiuk
Keyword(s):  
Hamiltonian System ◽  
Hamiltonian Systems ◽  
Homoclinic Orbits ◽  
Second Order ◽  
Singular Points ◽  
Global Maximum ◽  
Strong Force ◽  
Second Order Hamiltonian Systems ◽  
Order Hamiltonian System ◽  
Second Order Hamiltonian System

AbstractWe consider a conservative second order Hamiltonian system $$\ddot q + \nabla V(q) = 0$$ in ℝ3 with a potential V having a global maximum at the origin and a line l ∩ {0} = ϑ as a set of singular points. Under a certain compactness condition on V at infinity and a strong force condition at singular points we study, by the use of variational methods and geometrical arguments, the existence of homoclinic solutions of the system.

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.

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