Asymptotically almost periodic solutions for certain differential equations with piecewise constant arguments
Abstract It is well known that differential equations with piecewise constant arguments is a class of functional differential equations, which has fascinated many scholars in recent years. These delay differential equations have been successfully applied to diverse models in real life, especially in...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-05-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-020-02699-6 |
| _version_ | 1818534738693980160 |
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| author | Zonghong Feng Yong Wang Xin Ma |
| author_facet | Zonghong Feng Yong Wang Xin Ma |
| author_sort | Zonghong Feng |
| collection | DOAJ |
| description | Abstract It is well known that differential equations with piecewise constant arguments is a class of functional differential equations, which has fascinated many scholars in recent years. These delay differential equations have been successfully applied to diverse models in real life, especially in biology, physics, economics, etc. In this work, we are interested in the existence and uniqueness of asymptotically almost periodic solution for certain differential equation with piecewise constant arguments. Due to the particularity of the equations, we cannot use the traditional method to convert it into the difference equation with exponential dichotomy. Through constructing Cauchy matrix of the investigated system to find the corresponding Green matrix of the difference equation, we need the concept of exponential dichotomy and the Banach contraction fixed point theorem of the corresponding system. Then we give some sufficient conditions to obtain the existence and uniqueness of asymptotically almost periodic solutions for these systems. |
| first_indexed | 2024-12-11T18:15:28Z |
| format | Article |
| id | doaj.art-870354d46412412d8e836efbdc482765 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-11T18:15:28Z |
| publishDate | 2020-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-870354d46412412d8e836efbdc4827652022-12-22T00:55:26ZengSpringerOpenAdvances in Difference Equations1687-18472020-05-012020112210.1186/s13662-020-02699-6Asymptotically almost periodic solutions for certain differential equations with piecewise constant argumentsZonghong Feng0Yong Wang1Xin Ma2School of Mathematics and Physics, Lanzhou Jiaotong UniversitySchool of Sciences, Southwest Petroleum UniversitySchool of Science, Southwest University of Science and TechnologyAbstract It is well known that differential equations with piecewise constant arguments is a class of functional differential equations, which has fascinated many scholars in recent years. These delay differential equations have been successfully applied to diverse models in real life, especially in biology, physics, economics, etc. In this work, we are interested in the existence and uniqueness of asymptotically almost periodic solution for certain differential equation with piecewise constant arguments. Due to the particularity of the equations, we cannot use the traditional method to convert it into the difference equation with exponential dichotomy. Through constructing Cauchy matrix of the investigated system to find the corresponding Green matrix of the difference equation, we need the concept of exponential dichotomy and the Banach contraction fixed point theorem of the corresponding system. Then we give some sufficient conditions to obtain the existence and uniqueness of asymptotically almost periodic solutions for these systems.http://link.springer.com/article/10.1186/s13662-020-02699-6Asymptotically almost periodicDifferential equations with piecewise constant argumentsBanach contraction fixed point theoremExponential dichotomy |
| spellingShingle | Zonghong Feng Yong Wang Xin Ma Asymptotically almost periodic solutions for certain differential equations with piecewise constant arguments Advances in Difference Equations Asymptotically almost periodic Differential equations with piecewise constant arguments Banach contraction fixed point theorem Exponential dichotomy |
| title | Asymptotically almost periodic solutions for certain differential equations with piecewise constant arguments |
| title_full | Asymptotically almost periodic solutions for certain differential equations with piecewise constant arguments |
| title_fullStr | Asymptotically almost periodic solutions for certain differential equations with piecewise constant arguments |
| title_full_unstemmed | Asymptotically almost periodic solutions for certain differential equations with piecewise constant arguments |
| title_short | Asymptotically almost periodic solutions for certain differential equations with piecewise constant arguments |
| title_sort | asymptotically almost periodic solutions for certain differential equations with piecewise constant arguments |
| topic | Asymptotically almost periodic Differential equations with piecewise constant arguments Banach contraction fixed point theorem Exponential dichotomy |
| url | http://link.springer.com/article/10.1186/s13662-020-02699-6 |
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