On the mild solutions of higher-order differential equations in Banach spaces
For the higher-order abstract differential equation u(n)(t)=Au(t)+f(t), t∈ℝ, we give a new definition of mild solutions. We then characterize the regular admissibility of a translation-invariant subspace ℳ of BUC(ℝ,E) with respect to the above-mentioned equation in terms of solvability of the opera...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2003-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/S1085337503303057 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832548029035446272 |
|---|---|
| author | Nguyen Thanh Lan |
| author_facet | Nguyen Thanh Lan |
| author_sort | Nguyen Thanh Lan |
| collection | DOAJ |
| description | For the higher-order abstract differential equation u(n)(t)=Au(t)+f(t), t∈ℝ, we give a new definition of mild solutions. We then characterize the regular admissibility of a translation-invariant subspace ℳ of BUC(ℝ,E) with respect to the above-mentioned equation in terms of solvability of the operator equation AX−X𝒟n=C. As applications, periodicity and almost periodicity of mild solutions are also proved. |
| format | Article |
| id | doaj-art-010ce6e092d8422ebde7a6511acc2ed0 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2003-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-010ce6e092d8422ebde7a6511acc2ed02025-02-03T06:42:17ZengWileyAbstract and Applied Analysis1085-33751687-04092003-01-0120031586588010.1155/S1085337503303057On the mild solutions of higher-order differential equations in Banach spacesNguyen Thanh Lan0Department of Mathematics, Western Kentucky University, Bowling Green 42101, KY, USAFor the higher-order abstract differential equation u(n)(t)=Au(t)+f(t), t∈ℝ, we give a new definition of mild solutions. We then characterize the regular admissibility of a translation-invariant subspace ℳ of BUC(ℝ,E) with respect to the above-mentioned equation in terms of solvability of the operator equation AX−X𝒟n=C. As applications, periodicity and almost periodicity of mild solutions are also proved.http://dx.doi.org/10.1155/S1085337503303057 |
| spellingShingle | Nguyen Thanh Lan On the mild solutions of higher-order differential equations in Banach spaces Abstract and Applied Analysis |
| title | On the mild solutions of higher-order differential equations in Banach spaces |
| title_full | On the mild solutions of higher-order differential equations in Banach spaces |
| title_fullStr | On the mild solutions of higher-order differential equations in Banach spaces |
| title_full_unstemmed | On the mild solutions of higher-order differential equations in Banach spaces |
| title_short | On the mild solutions of higher-order differential equations in Banach spaces |
| title_sort | on the mild solutions of higher order differential equations in banach spaces |
| url | http://dx.doi.org/10.1155/S1085337503303057 |
| work_keys_str_mv | AT nguyenthanhlan onthemildsolutionsofhigherorderdifferentialequationsinbanachspaces |