A prescribed-energy problem for a conservative singular Hamiltonian system

1994 ◽  
Vol 128 (2) ◽  
pp. 127-164 ◽  
Author(s):  
Kazunaga Tanaka
Keyword(s):  
Hamiltonian System ◽  
Energy Problem ◽  
Singular Hamiltonian System

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.

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