Variational approach to some damped Dirichlet nonlinear impulsive differential equations

2011 ◽  
Vol 348 (2) ◽  
pp. 369-377 ◽  
Author(s):  
Jing Xiao ◽  
Juan J. Nieto
Keyword(s):  
Differential Equations ◽  
Variational Approach ◽  
Impulsive Differential Equations

scholarly journals Variational Approach to Impulsive Differential Equations with Singular Nonlinearities

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Naima Daoudi-Merzagui ◽  
Abdelkader Boucherif
Keyword(s):  
Differential Equations ◽  
Variational Method ◽  
Periodic Solutions ◽  
Variational Approach ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Second Order ◽  
Second Order Differential Equations ◽  
Singular Nonlinearities ◽  
Existence Of Periodic Solutions

We discuss the existence of periodic solutions for nonautonomous second order differential equations with singular nonlinearities. Simple sufficient conditions that enable us to obtain many distinct periodic solutions are provided. Our approach is based on a variational method.

scholarly journals Variational Approach to Impulsive Problems: A Survey of Recent Results

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Fang-fang Liao ◽  
Juntao Sun
Keyword(s):  
Differential Equations ◽  
Variational Methods ◽  
Boundary Value Problems ◽  
Periodic Solutions ◽  
Variational Approach ◽  
Boundary Value ◽  
Impulsive Differential Equations ◽  
Homoclinic Solutions ◽  
Nontrivial Solutions ◽  
Impulsive Problems

We present a survey on the existence of nontrivial solutions to impulsive differential equations by using variational methods, including solutions to boundary value problems, periodic solutions, and homoclinic solutions.

scholarly journals RETRACTION NOTICE TO “PERIODIC SOLUTIONS OF SECOND ORDER IMPULSIVE DIFFERENTIAL EQUATIONS AT RESONANCE VIA VARIATIONAL APPROACH” [MATH. MODEL. ANAL. 19(5):664–675, 2014]

2015 ◽  
Vol 20 (2) ◽  
pp. 289-289
Author(s):  
Jin Li ◽  
Jianlin Luo ◽  
Zaihong Wang
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Variational Approach ◽  
Impulsive Differential Equations ◽  
Second Order ◽  
Math Model ◽  
At Resonance ◽  
Retraction Notice

Retraction notice to “Periodic Solutions of Second Order Impulsive Differential Equations at Resonance via Variational Approach” [Math. Model. Anal. 19(5):664–675, 2014]

Variational Approach to Impulsive Differential Equations Using the Semi-Inverse Method

2011 ◽  
Vol 66 (10-11) ◽  
pp. 632-634 ◽  
Author(s):  
Ji-Huan He
Keyword(s):  
Variational Principle ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Variational Approach ◽  
Inverse Method ◽  
Dirichlet Boundary ◽  
Impulsive Differential Equations ◽  
Dirichlet Boundary Value Problem ◽  
Natural Conditions

The semi-inverse method is used to establish a variational principle for the Dirichlet boundary value problem with impulses. All the boundary conditions can be obtained as natural conditions by making the variational principle stationary.

scholarly journals RETRACTED ARTICLE: PERIODIC SOLUTIONS OF SECOND ORDER IMPULSIVE DIFFERENTIAL EQUATIONS AT RESONANCE VIA VARIATIONAL APPROACH

2014 ◽  
Vol 19 (5) ◽  
pp. 664-675 ◽  
Author(s):  
Jin Li ◽  
Jianlin Luo ◽  
Zaihong Wang
Keyword(s):  
Differential Equations ◽  
Variational Method ◽  
Periodic Solutions ◽  
Variational Approach ◽  
Impulsive Differential Equations ◽  
Second Order ◽  
Type Condition ◽  
At Resonance ◽  
Retracted Article ◽  
Existence Of Periodic Solutions

In this paper, we study the existence of periodic solutions of second order impulsive dierential equations at resonance. We prove the existence of periodic solutions under a generalized Landesman{Lazer type condition by using variational method.

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