Stability of Nonlinear Neutral Stochastic Functional Differential Equations
Neutral stochastic functional differential equations (NSFDEs) have recently been studied intensively. The well-known conditions imposed for the existence and uniqueness and exponential stability of the global solution are the local Lipschitz condition and the linear growth condition. Therefore, the...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2010/425762 |
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| _version_ | 1832564132864327680 |
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| author | Minggao Xue Shaobo Zhou Shigeng Hu |
| author_facet | Minggao Xue Shaobo Zhou Shigeng Hu |
| author_sort | Minggao Xue |
| collection | DOAJ |
| description | Neutral stochastic functional differential equations (NSFDEs) have recently been studied intensively. The well-known conditions imposed for the existence and uniqueness and exponential stability of the global solution are the local Lipschitz condition and the linear growth condition. Therefore, the existing results cannot be applied to many important nonlinear NSFDEs. The main aim of this paper is to remove the linear growth condition and establish a Khasminskii-type test for nonlinear NSFDEs. New criteria not only cover a wide class of highly nonlinear NSFDEs but they can also be verified much more easily than the classical criteria. Finally, several examples are given to illustrate main results. |
| format | Article |
| id | doaj-art-88dcb57cb2ea46599afce5766b41979c |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-88dcb57cb2ea46599afce5766b41979c2025-02-03T01:11:48ZengWileyJournal of Applied Mathematics1110-757X1687-00422010-01-01201010.1155/2010/425762425762Stability of Nonlinear Neutral Stochastic Functional Differential EquationsMinggao Xue0Shaobo Zhou1Shigeng Hu2School of Management, Huazhong University of Science and Technology, Wuhan 430074, ChinaSchool of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, ChinaSchool of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, ChinaNeutral stochastic functional differential equations (NSFDEs) have recently been studied intensively. The well-known conditions imposed for the existence and uniqueness and exponential stability of the global solution are the local Lipschitz condition and the linear growth condition. Therefore, the existing results cannot be applied to many important nonlinear NSFDEs. The main aim of this paper is to remove the linear growth condition and establish a Khasminskii-type test for nonlinear NSFDEs. New criteria not only cover a wide class of highly nonlinear NSFDEs but they can also be verified much more easily than the classical criteria. Finally, several examples are given to illustrate main results.http://dx.doi.org/10.1155/2010/425762 |
| spellingShingle | Minggao Xue Shaobo Zhou Shigeng Hu Stability of Nonlinear Neutral Stochastic Functional Differential Equations Journal of Applied Mathematics |
| title | Stability of Nonlinear Neutral Stochastic Functional Differential Equations |
| title_full | Stability of Nonlinear Neutral Stochastic Functional Differential Equations |
| title_fullStr | Stability of Nonlinear Neutral Stochastic Functional Differential Equations |
| title_full_unstemmed | Stability of Nonlinear Neutral Stochastic Functional Differential Equations |
| title_short | Stability of Nonlinear Neutral Stochastic Functional Differential Equations |
| title_sort | stability of nonlinear neutral stochastic functional differential equations |
| url | http://dx.doi.org/10.1155/2010/425762 |
| work_keys_str_mv | AT minggaoxue stabilityofnonlinearneutralstochasticfunctionaldifferentialequations AT shaobozhou stabilityofnonlinearneutralstochasticfunctionaldifferentialequations AT shigenghu stabilityofnonlinearneutralstochasticfunctionaldifferentialequations |