scholarly journals Existence of periodic solutions for two types of second-order nonlinear neutral integro-differential equations with infinite distributed mixed-delays

2018 ◽  
pp. 184-194
Author(s):  
Abdelouaheb Ardjouni ◽  
Hocine Gabsi ◽  
Ahcene Djoudi
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Second Order ◽  
Mixed Delays ◽  
Existence Of Periodic Solutions

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 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 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 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.

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