scholarly journals Infinitely many periodic solutions of planar Hamiltonian systems via the Poincaré–Birkhoff theorem

2018 ◽  
Vol 2018 (1) ◽  
Author(s):  
Zaihong Wang ◽  
Tiantian Ma
Keyword(s):  
Periodic Solutions ◽  
Hamiltonian Systems ◽  
Birkhoff Theorem ◽  
Infinitely Many Periodic Solutions

scholarly journals Infinitely Many Periodic Solutions for Nonautonomous Sublinear Second-Order Hamiltonian Systems

2010 ◽  
Vol 2010 ◽  
pp. 1-10 ◽  
Author(s):  
Peng Zhang ◽  
Chun-Lei Tang
Keyword(s):  
Periodic Solutions ◽  
Hamiltonian Systems ◽  
Critical Points ◽  
Local Minimum ◽  
Second Order ◽  
The Other ◽  
Second Order Hamiltonian Systems ◽  
Minimax Methods ◽  
Infinitely Many Periodic Solutions ◽  
Minimum Points

Two sequences of distinct periodic solutions for second-order Hamiltonian systems with sublinear nonlinearity are obtained by using the minimax methods. One sequence of solutions is local minimum points of functional, and the other is minimax type critical points of functional. We do not assume any symmetry condition on nonlinearity.

Infinitely many periodic solutions of non-autonomous second-order Hamiltonian systems

2014 ◽  
Vol 144 (1) ◽  
pp. 205-223 ◽  
Author(s):  
Yiwei Ye ◽  
Chun-Lei Tang
Keyword(s):  
Periodic Solutions ◽  
Hamiltonian Systems ◽  
Point Theory ◽  
Second Order ◽  
Mountain Pass Lemma ◽  
Fountain Theorem ◽  
Second Order Hamiltonian Systems ◽  
Minimax Methods ◽  
Symmetric Mountain Pass Lemma ◽  
Infinitely Many Periodic Solutions

In this paper, we study the existence of infinitely many periodic solutions for the non-autonomous second-order Hamiltonian systems with symmetry. Based on the minimax methods in critical point theory, in particular, the fountain theorem of Bartsch and the symmetric mountain pass lemma due to Kajikiya, we obtain the existence results for both the superquadratic case and the subquadratic case, which unify and sharply improve some recent results in the literature.

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