scholarly journals Existence of Periodic Solutions for a Class of Discrete Hamiltonian Systems

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Qiongfen Zhang ◽  
X. H. Tang ◽  
Qi-Ming Zhang
Keyword(s):  
Positive Integer ◽  
Critical Point ◽  
Periodic Solutions ◽  
Hamiltonian Systems ◽  
Critical Point Theory ◽  
Point Theory ◽  
Minimax Methods ◽  
Existence Of Periodic Solutions

By applying minimax methods in critical point theory, we prove the existence of periodic solutions for the following discrete Hamiltonian systemsΔ2u(t-1)+∇F(t,u(t))=0, wheret∈ℤ,u∈ℝN,F:ℤ×ℝN→ℝ,F(t,x)is continuously differentiable inxfor everyt∈ℤand isT-periodic int;Tis a positive integer.

scholarly journals Periodic Solutions for a Class of Singular Hamiltonian Systems on Time Scales

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Xiaofang Meng ◽  
Yongkun Li
Keyword(s):  
Variational Methods ◽  
Critical Point ◽  
Periodic Solutions ◽  
Hamiltonian Systems ◽  
Time Scales ◽  
Critical Point Theory ◽  
Point Theory ◽  
Singular Hamiltonian Systems ◽  
Existence Of Periodic Solutions

We are concerned with a class of singular Hamiltonian systems on time scales. Some results on the existence of periodic solutions are obtained for the system under consideration by means of the variational methods and the critical point theory.

scholarly journals Periodic Solutions for Second-Order Ordinary Differential Equations with Linear Nonlinearity

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Xiaohong Hu ◽  
Dabin Wang ◽  
Changyou Wang
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Critical Point ◽  
Periodic Solutions ◽  
Critical Point Theory ◽  
Point Theory ◽  
Second Order ◽  
Minimax Methods ◽  
Existence Of Periodic Solutions

By using minimax methods in critical point theory, we obtain the existence of periodic solutions for second-order ordinary differential equations with linear nonlinearity.

Infinitely many periodic solutions for ordinary p-Laplacian systems

2015 ◽  
Vol 4 (4) ◽  
pp. 251-261 ◽  
Author(s):  
Chun Li ◽  
Ravi P. Agarwal ◽  
Chun-Lei Tang
Keyword(s):  
Critical Point ◽  
Periodic Solutions ◽  
Critical Point Theory ◽  
Existence Theorems ◽  
Point Theory ◽  
Minimax Methods ◽  
Infinitely Many Periodic Solutions

AbstractSome existence theorems are obtained for infinitely many periodic solutions of ordinary p-Laplacian systems by minimax methods in critical point theory.

scholarly journals Periodic Solutions of Second-Order Differential Inclusions Systems with -Laplacian

2012 ◽  
Vol 2012 ◽  
pp. 1-24
Author(s):  
Liang Zhang ◽  
Peng Zhang
Keyword(s):  
Critical Point ◽  
Periodic Solutions ◽  
Critical Point Theory ◽  
Differential Inclusions ◽  
Point Theory ◽  
Existence Results ◽  
Second Order ◽  
Nonsmooth Critical Point Theory ◽  
Nonsmooth Critical Point ◽  
Existence Of Periodic Solutions

The existence of periodic solutions for nonautonomous second-order differential inclusion systems with -Laplacian is considered. We get some existence results of periodic solutions for system, a.e. , , by using nonsmooth critical point theory. Our results generalize and improve some theorems in the literature.

Periodic solutions of higher-dimensional discrete systems

2004 ◽  
Vol 134 (5) ◽  
pp. 1013-1022 ◽  
Author(s):  
Zhan Zhou ◽  
Jianshe Yu ◽  
Zhiming Guo
Keyword(s):  
Positive Integer ◽  
Critical Point ◽  
Periodic Solutions ◽  
Critical Point Theory ◽  
Discrete System ◽  
Discrete Systems ◽  
Point Theory ◽  
Second Order ◽  
Higher Dimensional ◽  
Image Position

Consider the second-order discrete system where f ∈ C (R × Rm, Rm), f(t + M, Z) = f(t, Z) for any (t, Z) ∈ R × Rm and M is a positive integer. By making use of critical-point theory, the existence of M-periodic solutions of (*) is obtained.

scholarly journals Existence of periodic solutions with prescribed minimal period of a 2nth-order discrete system

2019 ◽  
Vol 17 (1) ◽  
pp. 1392-1399
Author(s):  
Xia Liu ◽  
Tao Zhou ◽  
Haiping Shi
Keyword(s):  
Critical Point ◽  
Periodic Solutions ◽  
Critical Point Theory ◽  
Discrete System ◽  
Sufficient Conditions ◽  
Point Theory ◽  
Minimal Period ◽  
Existence Of Periodic Solutions ◽  
First Time

Abstract In this paper, we concern with a 2nth-order discrete system. Using the critical point theory, we establish various sets of sufficient conditions for the existence of periodic solutions with prescribed minimal period. To the best of our knowledge, this is the first time to discuss the periodic solutions with prescribed minimal period for a 2nth-order discrete system.

Existence of Periodic Solutions for a Class of Second-Order Nonlinear Difference Systems

2011 ◽  
Vol 148-149 ◽  
pp. 1164-1169
Author(s):  
Wei Ming Tan ◽  
Fang Su
Keyword(s):  
Critical Point ◽  
Periodic Solutions ◽  
Critical Point Theory ◽  
Point Theory ◽  
Second Order ◽  
Sufficient Condition ◽  
Order Difference ◽  
Difference Systems ◽  
Existence Of Periodic Solutions

In this paper, by using critical point theory, a sufficient condition is obtained on the existence of periodic solutions for a class of nonlinear second-order difference systems.

scholarly journals Existence of Periodic Solutions for a Class of Difference Systems withp-Laplacian

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
Kai Chen ◽  
Qiongfen Zhang
Keyword(s):  
Periodic Solutions ◽  
Critical Point Theory ◽  
Existence Theorems ◽  
Point Theory ◽  
Least Action Principle ◽  
Least Action ◽  
The Least Action Principle ◽  
Minimax Methods ◽  
Difference Systems ◽  
Existence Of Periodic Solutions

By applying the least action principle and minimax methods in critical point theory, we prove the existence of periodic solutions for a class of difference systems withp-Laplacian and obtain some existence theorems.

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