Oscillatory Periodic Solutions for Two Differential-Difference Equations Arising in Applications

We study the existence of oscillatory periodic solutions for two nonautonomous differential-difference equations which arise in a variety of applications with the following forms: ẋ(t)=-f(t,x(t-r)) and ẋ(t)=-f(t,x(t-s))-f(t,x(t-2s)), where f∈C(R×R,R) is odd with respect to x, and r,s>0 are two...

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Main Author: Rong Cheng
Format: Article
Language:English
Published: Wiley 2011-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2011/635926
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author Rong Cheng
author_facet Rong Cheng
author_sort Rong Cheng
collection DOAJ
description We study the existence of oscillatory periodic solutions for two nonautonomous differential-difference equations which arise in a variety of applications with the following forms: ẋ(t)=-f(t,x(t-r)) and ẋ(t)=-f(t,x(t-s))-f(t,x(t-2s)), where f∈C(R×R,R) is odd with respect to x, and r,s>0 are two given constants. By using a symplectic transformation constructed by Cheng (2010) and a result in Hamiltonian systems, the existence of oscillatory periodic solutions of the above-mentioned equations is established.
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spelling doaj-art-c062bc5b420e40dd9b139f788949810a2025-08-20T02:19:26ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/635926635926Oscillatory Periodic Solutions for Two Differential-Difference Equations Arising in ApplicationsRong Cheng0College of Mathematics and Physics, Nanjing University of Information Science and Technology, Nanjing 210044, ChinaWe study the existence of oscillatory periodic solutions for two nonautonomous differential-difference equations which arise in a variety of applications with the following forms: ẋ(t)=-f(t,x(t-r)) and ẋ(t)=-f(t,x(t-s))-f(t,x(t-2s)), where f∈C(R×R,R) is odd with respect to x, and r,s>0 are two given constants. By using a symplectic transformation constructed by Cheng (2010) and a result in Hamiltonian systems, the existence of oscillatory periodic solutions of the above-mentioned equations is established.http://dx.doi.org/10.1155/2011/635926
spellingShingle Rong Cheng
Oscillatory Periodic Solutions for Two Differential-Difference Equations Arising in Applications
Abstract and Applied Analysis
title Oscillatory Periodic Solutions for Two Differential-Difference Equations Arising in Applications
title_full Oscillatory Periodic Solutions for Two Differential-Difference Equations Arising in Applications
title_fullStr Oscillatory Periodic Solutions for Two Differential-Difference Equations Arising in Applications
title_full_unstemmed Oscillatory Periodic Solutions for Two Differential-Difference Equations Arising in Applications
title_short Oscillatory Periodic Solutions for Two Differential-Difference Equations Arising in Applications
title_sort oscillatory periodic solutions for two differential difference equations arising in applications
url http://dx.doi.org/10.1155/2011/635926
work_keys_str_mv AT rongcheng oscillatoryperiodicsolutionsfortwodifferentialdifferenceequationsarisinginapplications