scholarly journals Periodic solutions of a discrete Hamiltonian system with a change of sign in the potential

2006 ◽  
Vol 324 (2) ◽  
pp. 1140-1151 ◽  
Author(s):  
Jianshe Yu ◽  
Xiaoqing Deng ◽  
Zhiming Guo
Keyword(s):  
Hamiltonian System ◽  
Periodic Solutions ◽  
Discrete Hamiltonian System

Study on the Periodic Solutions to a Superquadratic Discrete Hamiltonian System Based on Mechanics

2013 ◽  
Vol 394 ◽  
pp. 92-95
Author(s):  
Da Wei Sun ◽  
Jia Rui Liu
Keyword(s):  
Hamiltonian System ◽  
Variational Methods ◽  
Periodic Solutions ◽  
Existence Of Solution ◽  
Discrete Hamiltonian System ◽  
New Type ◽  
Discrete Type

This paper studies the periodic solutions to a superquadratic second-oder discrete type Hamiltonian system in the n dimensional Euclide space. By the variational methods and some discrete computional techniques, this paper proves the existence of solution to a new type discrete Hamiltonian system.

Non-constant periodic solutions for second order Hamiltonian system with a p-Laplacian

2012 ◽  
Vol 62 (2) ◽  
Author(s):  
Xingyong Zhang ◽  
Xianhua Tang
Keyword(s):  
Hamiltonian System ◽  
Periodic Solutions ◽  
Existence Theorems ◽  
Second Order ◽  
Linking Theorem ◽  
Order Hamiltonian System ◽  
Second Order Hamiltonian System

AbstractIn this paper, some existence theorems are obtained for nonconstant periodic solutions of second order Hamiltonian system with a p-Laplacian by using the Linking Theorem.

scholarly journals Periodic solutions with prescribed minimal period for second order even Hamiltonian systems

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Juhong Kuang ◽  
Weiyi Chen ◽  
Zhiming Guo
Keyword(s):  
Hamiltonian System ◽  
Periodic Solutions ◽  
Convergent Subsequence ◽  
Step Length ◽  
Continuous Functions ◽  
Second Order ◽  
Limit Function ◽  
Minimal Period ◽  
Nonnegative Solutions ◽  
Convexity Assumptions

<p style='text-indent:20px;'>In this paper, we develop a new method to study Rabinowitz's conjecture on the existence of periodic solutions with prescribed minimal period for second order even Hamiltonian system without any convexity assumptions. Specifically, we first study the associated homogenous Dirichlet boundary value problems for the discretization of the Hamiltonian system with given step length and obtain a sequence of nonnegative solutions corresponding to different step lengths by using discrete variational methods. Then, using the sequence of nonnegative solutions, we construct a sequence of continuous functions which can be shown to be precompact. Finally, by utilizing the limit function of convergent subsequence and the symmetry of the potential, we will obtain the desired periodic solution. In particular, we prove Rabinowitz's conjecture in the case when the potential satisfies a certain symmetric assumption. Moreover, our main result greatly improves the related results in the literature in the case where <inline-formula><tex-math id="M1">\begin{document}$ N = 1 $\end{document}</tex-math></inline-formula>.</p>

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