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 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 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.

scholarly journals Multiple Periodic Solutions for a Class of Second-Order Neutral Impulsive Functional Differential Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-5
Author(s):  
Jingli Xie ◽  
Zhiguo Luo ◽  
Yuhua Zeng
Keyword(s):  
Differential Equations ◽  
Variational Methods ◽  
Critical Point ◽  
Periodic Solutions ◽  
Critical Point Theory ◽  
Functional Differential Equations ◽  
Point Theory ◽  
Second Order ◽  
Multiple Periodic Solutions ◽  
Functional Differential

In this paper, we study a class of second-order neutral impulsive functional differential equations. Under certain conditions, we establish the existence of multiple periodic solutions by means of critical point theory and variational methods. We propose an example to illustrate the applicability of our result.

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.

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 Asymptoticallyp-Linear Discrete Systems Involvingp-Laplacian

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Kai Chen ◽  
Qiongfen Zhang
Keyword(s):  
Critical Point ◽  
Periodic Solutions ◽  
Critical Point Theory ◽  
Discrete System ◽  
Mountain Pass Theorem ◽  
Discrete Systems ◽  
Point Theory ◽  
Existence Results ◽  
Existence Of Periodic Solutions ◽  
Linear Discrete Systems

By applying Mountain Pass Theorem in critical point theory, two existence results are obtained for the following asymptoticallyp-linearp-Laplacian discrete systemΔ(|Δu(t−1)|p−2Δu(t−1))+∇[−K(t,u(t))+W(t,u(t))]=0. The results obtained generalize some known works.

scholarly journals Existence and Multiplicity of Periodic Solutions Generated by Impulses

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Liu Yang ◽  
Haibo Chen
Keyword(s):  
Variational Methods ◽  
Critical Point ◽  
Periodic Solutions ◽  
Critical Point Theory ◽  
Point Theory ◽  
Second Order ◽  
Differential Systems ◽  
Existence And Multiplicity ◽  
Infinitely Many Periodic Solutions

We investigate the existence and multiplicity of periodic solutions for a class of second-order differential systems with impulses. By using variational methods and critical point theory, we obtain such a system possesses at least one nonzero, two nonzero, or infinitely many periodic solutions generated by impulses under different conditions, respectively. Recent results in the literature are generalized and significantly improved.

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