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 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 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.

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 Subharmonic Solutions for a Class of Second-Orderp-Laplacian Systems with Impulsive Effects

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Wen-Zhen Gong ◽  
Qiongfen Zhang ◽  
X. H. Tang
Keyword(s):  
Critical Point ◽  
Periodic Solutions ◽  
Existence Theorem ◽  
Critical Point Theory ◽  
Point Theory ◽  
Second Order ◽  
Impulsive Effects ◽  
Subharmonic Solutions ◽  
Minimax Methods ◽  
Infinitely Many Periodic Solutions

By using minimax methods in critical point theory, a new existence theorem of infinitely many periodic solutions is obtained for a class of second-orderp-Laplacian systems with impulsive effects. Our result generalizes many known works in the literature.

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 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 a System of Difference Equations

2009 ◽  
Vol 2009 ◽  
pp. 1-9 ◽  
Author(s):  
Shugui Kang ◽  
Bao Shi
Keyword(s):  
Nonlinear Systems ◽  
Critical Point ◽  
Periodic Solutions ◽  
Difference Equations ◽  
Critical Point Theory ◽  
Existence Theorems ◽  
Point Theory ◽  
Second Order ◽  
System Of Difference Equations

This paper deals with the second-order nonlinear systems of difference equations, we obtain the existence theorems of periodic solutions. The theorems are proved by using critical point theory.

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