scholarly journals Homoclinic Orbits for Asymptotically Linear Hamiltonian Systems

2001 ◽  
Vol 187 (1) ◽  
pp. 25-41 ◽  
Author(s):  
Andrzej Szulkin ◽  
Wenming Zou
Keyword(s):  
Hamiltonian Systems ◽  
Homoclinic Orbits ◽  
Asymptotically Linear ◽  
Linear Hamiltonian Systems

scholarly journals Homoclinic Orbits for a Class of Nonperiodic Hamiltonian Systems with Some Twisted Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Qi Wang ◽  
Qingye Zhang
Keyword(s):  
Hamiltonian Systems ◽  
Index Theory ◽  
Maslov Index ◽  
Homoclinic Orbits ◽  
Asymptotically Linear ◽  
Existence And Multiplicity ◽  
Hamiltonian Functions

By the Maslov index theory, we will study the existence and multiplicity of homoclinic orbits for a class of asymptotically linear nonperiodic Hamiltonian systems with some twisted conditions on the Hamiltonian functions.

Periodic Solutions of Asymptotically Linear Hamiltonian Systems without Twist Conditions

2010 ◽  
Vol 65 (5) ◽  
pp. 445-452
Author(s):  
Rong Cheng ◽  
Dongfeng Zhang
Keyword(s):  
Dynamical System ◽  
Periodic Solutions ◽  
Hamiltonian Systems ◽  
Galerkin Approximation ◽  
Point Theory ◽  
Dynamical System Theory ◽  
Hamiltonian Form ◽  
Asymptotically Linear ◽  
Linear Hamiltonian Systems ◽  
Existence Of Periodic Solutions

In dynamical system theory, especially in many fields of applications from mechanics, Hamiltonian systems play an important role, since many related equations in mechanics can be written in an Hamiltonian form. In this paper, we study the existence of periodic solutions for a class of Hamiltonian systems. By applying the Galerkin approximation method together with a result of critical point theory, we establish the existence of periodic solutions of asymptotically linear Hamiltonian systems without twist conditions. Twist conditions play crucial roles in the study of periodic solutions for asymptotically linear Hamiltonian systems. The lack of twist conditions brings some difficulty to the study. To the authors’ knowledge, very little is known about the case, where twist conditions do not hold.

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