Response Solutions for a Singularly Perturbed System Involving Reflection of the Argument

Response Solutions for a Singularly Perturbed System Involving Reflection of the Argument

In this paper, the existence and uniqueness of response solutions, which has the same frequency ω with the nonlinear terms, are investigated for a quasiperiodic singularly perturbed system involving reflection of the argument. Firstly, we prove that all quasiperiodic functions with the frequency ω f...

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Main Authors: Shanliang Zhu, Shufang Zhang, Xinli Zhang, Qingling Li
Format: Article
Language:English
Published: Hindawi Limited 2020-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2020/6738247
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spelling doaj-f200f9011ac841dfa39feec0b239b0932021-07-02T15:07:57ZengHindawi LimitedAdvances in Mathematical Physics1687-91201687-91392020-01-01202010.1155/2020/67382476738247Response Solutions for a Singularly Perturbed System Involving Reflection of the ArgumentShanliang Zhu0Shufang Zhang1Xinli Zhang2Qingling Li3College of Electromechanical Engineering, Qingdao University of Science and Technology, Qingdao 266061, ChinaSchool of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, ChinaSchool of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, ChinaCollege of Electromechanical Engineering, Qingdao University of Science and Technology, Qingdao 266061, ChinaIn this paper, the existence and uniqueness of response solutions, which has the same frequency ω with the nonlinear terms, are investigated for a quasiperiodic singularly perturbed system involving reflection of the argument. Firstly, we prove that all quasiperiodic functions with the frequency ω form a Banach space. Then, we obtain the existence and uniqueness of quasiperiodic solutions by means of the fixed-point methods and the B-property of quasiperiodic functions.http://dx.doi.org/10.1155/2020/6738247
collection DOAJ
language English
format Article
sources DOAJ
author Shanliang Zhu
Shufang Zhang
Xinli Zhang
Qingling Li
spellingShingle Shanliang Zhu
Shufang Zhang
Xinli Zhang
Qingling Li
Response Solutions for a Singularly Perturbed System Involving Reflection of the Argument
Advances in Mathematical Physics
author_facet Shanliang Zhu
Shufang Zhang
Xinli Zhang
Qingling Li
author_sort Shanliang Zhu
title Response Solutions for a Singularly Perturbed System Involving Reflection of the Argument
title_short Response Solutions for a Singularly Perturbed System Involving Reflection of the Argument
title_full Response Solutions for a Singularly Perturbed System Involving Reflection of the Argument
title_fullStr Response Solutions for a Singularly Perturbed System Involving Reflection of the Argument
title_full_unstemmed Response Solutions for a Singularly Perturbed System Involving Reflection of the Argument
title_sort response solutions for a singularly perturbed system involving reflection of the argument
publisher Hindawi Limited
series Advances in Mathematical Physics
issn 1687-9120
1687-9139
publishDate 2020-01-01
description In this paper, the existence and uniqueness of response solutions, which has the same frequency ω with the nonlinear terms, are investigated for a quasiperiodic singularly perturbed system involving reflection of the argument. Firstly, we prove that all quasiperiodic functions with the frequency ω form a Banach space. Then, we obtain the existence and uniqueness of quasiperiodic solutions by means of the fixed-point methods and the B-property of quasiperiodic functions.
url http://dx.doi.org/10.1155/2020/6738247
work_keys_str_mv AT shanliangzhu responsesolutionsforasingularlyperturbedsysteminvolvingreflectionoftheargument
AT shufangzhang responsesolutionsforasingularlyperturbedsysteminvolvingreflectionoftheargument
AT xinlizhang responsesolutionsforasingularlyperturbedsysteminvolvingreflectionoftheargument
AT qinglingli responsesolutionsforasingularlyperturbedsysteminvolvingreflectionoftheargument
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