Periodic Solutions of Duffing Equation with an Asymmetric Nonlinearity and a Deviating Argument

We study the existence of periodic solutions of the second-order differential equation x′′+ax+-bx-+g(x(t-τ))=p(t), where a,b are two constants satisfying 1/a+1/b=2/n, n∈N, τ is a constant satisfying 0≤τ<2π, g,p:R→R are continuous, and p is 2π-periodic. When the limits limx→±∞g(x)=g(±∞) exist and...

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Main Authors: Zaihong Wang, Jin Li, Tiantian Ma
Format: Article
Language:English
Published: Wiley 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/507854
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author Zaihong Wang
Jin Li
Tiantian Ma
author_facet Zaihong Wang
Jin Li
Tiantian Ma
author_sort Zaihong Wang
collection DOAJ
description We study the existence of periodic solutions of the second-order differential equation x′′+ax+-bx-+g(x(t-τ))=p(t), where a,b are two constants satisfying 1/a+1/b=2/n, n∈N, τ is a constant satisfying 0≤τ<2π, g,p:R→R are continuous, and p is 2π-periodic. When the limits limx→±∞g(x)=g(±∞) exist and are finite, we give some sufficient conditions for the existence of 2π-periodic solutions of the given equation.
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spelling doaj-art-313ed797241648a7b785be757f8bf69c2025-08-20T02:38:55ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/507854507854Periodic Solutions of Duffing Equation with an Asymmetric Nonlinearity and a Deviating ArgumentZaihong Wang0Jin Li1Tiantian Ma2School of Mathematical Sciences, Capital Normal University, Beijing 100048, ChinaSchool of Mathematical Sciences, Capital Normal University, Beijing 100048, ChinaSchool of Mathematical Sciences, Capital Normal University, Beijing 100048, ChinaWe study the existence of periodic solutions of the second-order differential equation x′′+ax+-bx-+g(x(t-τ))=p(t), where a,b are two constants satisfying 1/a+1/b=2/n, n∈N, τ is a constant satisfying 0≤τ<2π, g,p:R→R are continuous, and p is 2π-periodic. When the limits limx→±∞g(x)=g(±∞) exist and are finite, we give some sufficient conditions for the existence of 2π-periodic solutions of the given equation.http://dx.doi.org/10.1155/2013/507854
spellingShingle Zaihong Wang
Jin Li
Tiantian Ma
Periodic Solutions of Duffing Equation with an Asymmetric Nonlinearity and a Deviating Argument
Abstract and Applied Analysis
title Periodic Solutions of Duffing Equation with an Asymmetric Nonlinearity and a Deviating Argument
title_full Periodic Solutions of Duffing Equation with an Asymmetric Nonlinearity and a Deviating Argument
title_fullStr Periodic Solutions of Duffing Equation with an Asymmetric Nonlinearity and a Deviating Argument
title_full_unstemmed Periodic Solutions of Duffing Equation with an Asymmetric Nonlinearity and a Deviating Argument
title_short Periodic Solutions of Duffing Equation with an Asymmetric Nonlinearity and a Deviating Argument
title_sort periodic solutions of duffing equation with an asymmetric nonlinearity and a deviating argument
url http://dx.doi.org/10.1155/2013/507854
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AT jinli periodicsolutionsofduffingequationwithanasymmetricnonlinearityandadeviatingargument
AT tiantianma periodicsolutionsofduffingequationwithanasymmetricnonlinearityandadeviatingargument