Periodic solutions for a class of Duffing differential equations-Reference-Cited by-同舟云学术

Periodic solutions for a class of Duffing differential equations

Published:2019-06-01 Issue:1 Volume:5 Page:86-103
ISSN:2351-8227
Container-title:Moroccan Journal of Pure and Applied Analysis
language:en
Short-container-title:

Author:

Feddaoui Amina¹,Llibre Jaume²,Makhlouf Amar¹

Affiliation:

1. Department of Mathematics , University of Annaba , Laboratory LMA , P.O.Box 12, Annaba 23000 , Algeria

2. Departament de Matematiques , Universitat Aut`onoma de Barcelona , 08193 Bellaterra, Barcelona , Catalonia, Spain

Abstract

Abstract We provide sufficient conditions for the existence of periodic solutions for the class of Duffing differential equations

x ″ + c ( t ) x ′ + a ( t ) x + b ( t ) x 3 = h ( t , x ) ,

x'' + c(t)x' + a(t)x + b(t){x^3} = h(t,x),

where the functions a(t), b(t), c(t) and h(t, x) are C 2 and T–periodic in the variable t.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Control and Optimization,Numerical Analysis,Analysis

Link

https://www.sciendo.com/pdf/10.2478/mjpaa-2019-0007

Reference19 articles.

1. [1] R. Benterki and J. Llibre, Periodic solutions of the Duffing differential equation revisited via the averaging theory, J. of Nonlinear Modeling and Analysis 1 (2019), 10–26.

2. [2] R. Benterki and J. Llibre, Periodic solutions of a class of Duffing differential equations, to appear in J. of Nonlinear Modeling and Analysis.

3. [3] A. Buica, J.P. Françoise and J. Llibre, Periodic solutions of nonlinear periodic differential systems with a small parameter, Comm. Pure and Appl. Anal. 6 (2007), 103–111.

4. [4] H.B. Chen and Y. Li, Stability and exact multiplicity of periodic solutions of Duffing equations with cubic nonlinearities, Proc. Amer. Math. Soc. 135 (2007), 3925–3932.10.1090/S0002-9939-07-09024-7

5. [5] H. Chen and Y. Li, Rate of decay of stable periodic solutions of Duffing equations, J. Differential Equations 236 (2007), 493–503.10.1016/j.jde.2007.01.023

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1. Periodic Solutions for a Class of Duffing Differential Equations Via Averaging Theory;Differential Equations and Dynamical Systems;2023-06-29