scholarly journals A Note on the Minimal Period Problem for Second Order Hamiltonian Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Huafeng Xiao
Keyword(s):  
Periodic Solutions ◽  
Hamiltonian Systems ◽  
Sufficient Conditions ◽  
Nehari Manifold ◽  
Second Order ◽  
Minimal Period ◽  
Period Problem ◽  
Second Order Hamiltonian Systems

We study periodic solutions of second order Hamiltonian systems with even potential. By making use of generalized Nehari manifold, some sufficient conditions are obtained to guarantee the multiplicity and minimality of periodic solutions for second order Hamiltonian systems. Our results generalize the outcome in the literature.

scholarly journals Periodic solutions with prescribed minimal period to Hamiltonian systems

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Huafeng Xiao ◽  
Zupei Shen
Keyword(s):  
Periodic Solution ◽  
Periodic Solutions ◽  
Hamiltonian Systems ◽  
Nonlinear Term ◽  
Perturbation Technique ◽  
Nehari Manifold ◽  
Minimal Period ◽  
Variational Functional ◽  
Second Order Hamiltonian Systems ◽  
The Nehari Manifold

AbstractIn this article, we study the existence of periodic solutions to second order Hamiltonian systems. Our goal is twofold. When the nonlinear term satisfies a strictly monotone condition, we show that, for any $T>0$ T > 0 , there exists a T-periodic solution with minimal period T. When the nonlinear term satisfies a non-decreasing condition, using a perturbation technique, we prove a similar result. In the latter case, the periodic solution corresponds to a critical point which minimizes the variational functional on the Nehari manifold which is not homeomorphic to the unit sphere.

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