scholarly journals Subharmonic Solutions with Prescribed Minimal Periodic for a Class of Second-Order Impulsive Functional Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
Qi Wang ◽  
Dicheng Lu ◽  
Zhaoyue Zheng
Keyword(s):  
Differential Equations ◽  
Variational Methods ◽  
Critical Point ◽  
Critical Point Theory ◽  
Functional Differential Equations ◽  
Point Theory ◽  
Second Order ◽  
Minimal Period ◽  
Subharmonic Solutions ◽  
Functional Differential

By using critical point theory and variational methods, we investigate the subharmonic solutions with prescribed minimal period for a class of second-order impulsive functional differential equations. The conditions for the existence of subharmonic solutions are established. In the end, we provide an example to illustrate our main results.

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 Infinitely Many Homoclinic Solutions for Nonperiodic Fourth Order Differential Equations with General Potentials

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Liu Yang
Keyword(s):  
Differential Equations ◽  
Variational Methods ◽  
Critical Point ◽  
Fourth Order ◽  
Critical Point Theory ◽  
Point Theory ◽  
Homoclinic Solutions

We investigate a class of nonperiodic fourth order differential equations with general potentials. By using variational methods and genus properties in critical point theory, we obtain that such equations possess infinitely homoclinic solutions.

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 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.

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.

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