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scholarly journals RETRACTED ARTICLE: PERIODIC SOLUTIONS OF SECOND ORDER IMPULSIVE DIFFERENTIAL EQUATIONS AT RESONANCE VIA VARIATIONAL APPROACH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Retracted Article ◽  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

scholarly journals Periodic solutions for periodic second-order differential equations with variable potentials

2018 ◽  
Vol 24 (2) ◽  
pp. 127-137
Author(s):  
Jaume Llibre ◽  
Ammar Makhlouf
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Order Differential Equation ◽  
Sufficient Conditions ◽  
Second Order ◽  
Second Order Differential Equations ◽  
Second Order Differential Equation ◽  
Existence Of Periodic Solutions

Abstract We provide sufficient conditions for the existence of periodic solutions of the second-order differential equation with variable potentials {-(px^{\prime})^{\prime}(t)-r(t)p(t)x^{\prime}(t)+q(t)x(t)=f(t,x(t))} , where the functions {p(t)>0} , {q(t)} , {r(t)} and {f(t,x)} are {\mathcal{C}^{2}} and T-periodic in the variable t.

scholarly journals Subharmonic Solutions of Nonautonomous Second Order Differential Equations with Singular Nonlinearities

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
N. Daoudi-Merzagui ◽  
F. Derrab ◽  
A. Boucherif
Keyword(s):  
Differential Equations ◽  
Variational Method ◽  
Saddle Point ◽  
Point Theorem ◽  
Sufficient Conditions ◽  
Second Order ◽  
Saddle Point Theorem ◽  
Second Order Differential Equations ◽  
Subharmonic Solutions ◽  
Singular Nonlinearities

We discuss the existence of subharmonic solutions for nonautonomous second order differential equations with singular nonlinearities. Simple sufficient conditions are provided enable us to obtain infinitely many distinct subharmonic solutions. Our approach is based on a variational method, in particular the saddle point theorem.

scholarly journals Periodic solutions of Lienard differential equations via averaging theory of order two

2015 ◽  
Vol 87 (4) ◽  
pp. 1905-1913
Author(s):  
JAUME LLIBRE ◽  
DOUGLAS D. NOVAES ◽  
MARCO A. TEIXEIRA
Keyword(s):  
Positive Integer ◽  
Differential Equations ◽  
Periodic Function ◽  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Main Tool ◽  
Second Order ◽  
Averaging Theory ◽  
Existence Of Periodic Solutions

Abstract For ε ≠ 0sufficiently small we provide sufficient conditions for the existence of periodic solutions for the Lienard differential equations of the form x ′′ + f ( x ) x ′ + n 2 x + g ( x ) = ε 2 p 1 ( t ) + ε 3 p 2 ( t ) , where n is a positive integer, f : ℝ → ℝis a C 3function, g : ℝ → ℝis a C 4function, and p i : ℝ → ℝfor i = 1 , 2are continuous 2 π–periodic function. The main tool used in this paper is the averaging theory of second order. We also provide one application of the main result obtained.

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]

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