Periodic solutions for neutral functional differential equations with impulses on time scales
Let $mathbb{T}$ be a periodic time scale. We use Krasnoselskii's fixed point theorem to show that the neutral functional differential equation with impulses $$displaylines{ x^{Delta}(t)=-A(t)x^sigma(t)+g^Delta(t,x(t-h(t)))+f(t,x(t),x(t-h(t))),quad teq t_j,;tinmathbb{T},cr x(t_j^+)= x(t_j^...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Texas State University
2012-04-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2012/57/abstr.html |
| _version_ | 1818139626332749824 |
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| author | Yongkun Li Xiaoyan Dou Jianwen Zhou |
| author_facet | Yongkun Li Xiaoyan Dou Jianwen Zhou |
| author_sort | Yongkun Li |
| collection | DOAJ |
| description | Let $mathbb{T}$ be a periodic time scale. We use Krasnoselskii's fixed point theorem to show that the neutral functional differential equation with impulses $$displaylines{ x^{Delta}(t)=-A(t)x^sigma(t)+g^Delta(t,x(t-h(t)))+f(t,x(t),x(t-h(t))),quad teq t_j,;tinmathbb{T},cr x(t_j^+)= x(t_j^-)+I_j(x(t_j)), quad jin mathbb{Z}^+ }$$ has a periodic solution. Under a slightly more stringent conditions we show that the periodic solution is unique using the contraction mapping principle. |
| first_indexed | 2024-12-11T10:31:05Z |
| format | Article |
| id | doaj.art-7c280dcf1817412997d45b2e46e9bc1b |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-11T10:31:05Z |
| publishDate | 2012-04-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-7c280dcf1817412997d45b2e46e9bc1b2022-12-22T01:10:55ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912012-04-01201257,114Periodic solutions for neutral functional differential equations with impulses on time scalesYongkun LiXiaoyan DouJianwen ZhouLet $mathbb{T}$ be a periodic time scale. We use Krasnoselskii's fixed point theorem to show that the neutral functional differential equation with impulses $$displaylines{ x^{Delta}(t)=-A(t)x^sigma(t)+g^Delta(t,x(t-h(t)))+f(t,x(t),x(t-h(t))),quad teq t_j,;tinmathbb{T},cr x(t_j^+)= x(t_j^-)+I_j(x(t_j)), quad jin mathbb{Z}^+ }$$ has a periodic solution. Under a slightly more stringent conditions we show that the periodic solution is unique using the contraction mapping principle.http://ejde.math.txstate.edu/Volumes/2012/57/abstr.htmlPositive periodic solutionneutral functional differentialequationsimpulsesKrasnoselskii fixed pointtime scales |
| spellingShingle | Yongkun Li Xiaoyan Dou Jianwen Zhou Periodic solutions for neutral functional differential equations with impulses on time scales Electronic Journal of Differential Equations Positive periodic solution neutral functional differential equations impulses Krasnoselskii fixed point time scales |
| title | Periodic solutions for neutral functional differential equations with impulses on time scales |
| title_full | Periodic solutions for neutral functional differential equations with impulses on time scales |
| title_fullStr | Periodic solutions for neutral functional differential equations with impulses on time scales |
| title_full_unstemmed | Periodic solutions for neutral functional differential equations with impulses on time scales |
| title_short | Periodic solutions for neutral functional differential equations with impulses on time scales |
| title_sort | periodic solutions for neutral functional differential equations with impulses on time scales |
| topic | Positive periodic solution neutral functional differential equations impulses Krasnoselskii fixed point time scales |
| url | http://ejde.math.txstate.edu/Volumes/2012/57/abstr.html |
| work_keys_str_mv | AT yongkunli periodicsolutionsforneutralfunctionaldifferentialequationswithimpulsesontimescales AT xiaoyandou periodicsolutionsforneutralfunctionaldifferentialequationswithimpulsesontimescales AT jianwenzhou periodicsolutionsforneutralfunctionaldifferentialequationswithimpulsesontimescales |