Uniformly Almost Periodic Functions and Almost Periodic Solutions to Dynamic Equations on Time Scales
Firstly, we propose a concept of uniformly almost periodic functions on almost periodic time scales and investigate some basic properties of them. When time scale T=ℝ or ℤ, our definition of the uniformly almost periodic functions is equivalent to the classical definitions of uniformly almost period...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/341520 |
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| _version_ | 1832550714342113280 |
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| author | Yongkun Li Chao Wang |
| author_facet | Yongkun Li Chao Wang |
| author_sort | Yongkun Li |
| collection | DOAJ |
| description | Firstly, we propose a concept of uniformly almost periodic functions on almost periodic time scales and investigate some basic properties of them. When time scale T=ℝ or ℤ, our definition of the uniformly almost periodic functions is equivalent to the classical definitions of uniformly almost periodic functions and the uniformly almost periodic sequences, respectively. Then, based on these, we study the existence and uniqueness of almost periodic solutions and derive some fundamental conditions of admitting an exponential dichotomy to linear dynamic equations. Finally, as an application of our results, we study the existence of almost periodic solutions for an almost periodic nonlinear dynamic equations on time scales. |
| format | Article |
| id | doaj-art-a2105e4c93de473bba450a895c5eb72f |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-a2105e4c93de473bba450a895c5eb72f2025-02-03T06:06:03ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/341520341520Uniformly Almost Periodic Functions and Almost Periodic Solutions to Dynamic Equations on Time ScalesYongkun Li0Chao Wang1Department of Mathematics, Yunnan University, Yunnan, Kunming 650091, ChinaDepartment of Mathematics, Yunnan University, Yunnan, Kunming 650091, ChinaFirstly, we propose a concept of uniformly almost periodic functions on almost periodic time scales and investigate some basic properties of them. When time scale T=ℝ or ℤ, our definition of the uniformly almost periodic functions is equivalent to the classical definitions of uniformly almost periodic functions and the uniformly almost periodic sequences, respectively. Then, based on these, we study the existence and uniqueness of almost periodic solutions and derive some fundamental conditions of admitting an exponential dichotomy to linear dynamic equations. Finally, as an application of our results, we study the existence of almost periodic solutions for an almost periodic nonlinear dynamic equations on time scales.http://dx.doi.org/10.1155/2011/341520 |
| spellingShingle | Yongkun Li Chao Wang Uniformly Almost Periodic Functions and Almost Periodic Solutions to Dynamic Equations on Time Scales Abstract and Applied Analysis |
| title | Uniformly Almost Periodic Functions and Almost Periodic Solutions to Dynamic Equations on Time Scales |
| title_full | Uniformly Almost Periodic Functions and Almost Periodic Solutions to Dynamic Equations on Time Scales |
| title_fullStr | Uniformly Almost Periodic Functions and Almost Periodic Solutions to Dynamic Equations on Time Scales |
| title_full_unstemmed | Uniformly Almost Periodic Functions and Almost Periodic Solutions to Dynamic Equations on Time Scales |
| title_short | Uniformly Almost Periodic Functions and Almost Periodic Solutions to Dynamic Equations on Time Scales |
| title_sort | uniformly almost periodic functions and almost periodic solutions to dynamic equations on time scales |
| url | http://dx.doi.org/10.1155/2011/341520 |
| work_keys_str_mv | AT yongkunli uniformlyalmostperiodicfunctionsandalmostperiodicsolutionstodynamicequationsontimescales AT chaowang uniformlyalmostperiodicfunctionsandalmostperiodicsolutionstodynamicequationsontimescales |