Existence of Square-Mean Almost Automorphic Solutions to Stochastic Functional Integrodifferential Equations in Hilbert Spaces
The existence and uniqueness of square-mean almost automorphic mild solution to a stochastic functional integrodifferential equation is studied. Under some appropriate assumptions, the existence and uniqueness of square-mean almost automorphic mild solution is obtained by Banach’s fixed point theore...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/480241 |
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| author | Lijie Li |
| author_facet | Lijie Li |
| author_sort | Lijie Li |
| collection | DOAJ |
| description | The existence and uniqueness of square-mean almost automorphic mild solution to a stochastic functional integrodifferential equation is studied. Under some appropriate assumptions, the existence and uniqueness of square-mean almost automorphic mild solution is obtained by Banach’s fixed point theorem. Particularly, based on Schauder’s fixed point theorem, the existence of square-mean almost automorphic mild solution is obtained by using the condition which is weaker than Lipschitz conditions. Finally, an example illustrating our main result is given. |
| format | Article |
| id | doaj-art-5271311f010049e8840946234fb80184 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-5271311f010049e8840946234fb801842025-02-03T01:01:58ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/480241480241Existence of Square-Mean Almost Automorphic Solutions to Stochastic Functional Integrodifferential Equations in Hilbert SpacesLijie Li0School of Mathematics and Information Sciences, Yulin Normal University, Yulin 537000, ChinaThe existence and uniqueness of square-mean almost automorphic mild solution to a stochastic functional integrodifferential equation is studied. Under some appropriate assumptions, the existence and uniqueness of square-mean almost automorphic mild solution is obtained by Banach’s fixed point theorem. Particularly, based on Schauder’s fixed point theorem, the existence of square-mean almost automorphic mild solution is obtained by using the condition which is weaker than Lipschitz conditions. Finally, an example illustrating our main result is given.http://dx.doi.org/10.1155/2014/480241 |
| spellingShingle | Lijie Li Existence of Square-Mean Almost Automorphic Solutions to Stochastic Functional Integrodifferential Equations in Hilbert Spaces Abstract and Applied Analysis |
| title | Existence of Square-Mean Almost Automorphic Solutions to Stochastic Functional Integrodifferential Equations in Hilbert Spaces |
| title_full | Existence of Square-Mean Almost Automorphic Solutions to Stochastic Functional Integrodifferential Equations in Hilbert Spaces |
| title_fullStr | Existence of Square-Mean Almost Automorphic Solutions to Stochastic Functional Integrodifferential Equations in Hilbert Spaces |
| title_full_unstemmed | Existence of Square-Mean Almost Automorphic Solutions to Stochastic Functional Integrodifferential Equations in Hilbert Spaces |
| title_short | Existence of Square-Mean Almost Automorphic Solutions to Stochastic Functional Integrodifferential Equations in Hilbert Spaces |
| title_sort | existence of square mean almost automorphic solutions to stochastic functional integrodifferential equations in hilbert spaces |
| url | http://dx.doi.org/10.1155/2014/480241 |
| work_keys_str_mv | AT lijieli existenceofsquaremeanalmostautomorphicsolutionstostochasticfunctionalintegrodifferentialequationsinhilbertspaces |