LaSalle-Type Theorems for General Nonlinear Stochastic Functional Differential Equations by Multiple Lyapunov Functions
We investigate LaSalle-type theorems for general nonlinear stochastic functional differential equations. With some preliminaries on lemmas and the derivation techniques, we establish three LaSalle-type theorems for the general nonlinear stochastic functional differential equations via multiple Lyapu...
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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/10.1155/2014/486191 |
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| _version_ | 1832554253825081344 |
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| author | Xueyan Zhao Feiqi Deng Xiaojing Zhong |
| author_facet | Xueyan Zhao Feiqi Deng Xiaojing Zhong |
| author_sort | Xueyan Zhao |
| collection | DOAJ |
| description | We investigate LaSalle-type theorems for general nonlinear stochastic functional differential equations. With some preliminaries on lemmas and the derivation techniques, we establish three LaSalle-type theorems for the general nonlinear stochastic functional differential equations via multiple Lyapunov functions. For the typical special case with estimations involving |xt|p for the derivatives of the Lyapunov functions, a theorem is established as the corollary of the main theorem. At the end of the paper, an example is given to illustrate the usage of the method proposed and show the advantage of the results obtained. |
| format | Article |
| id | doaj-art-d7d567ab2b304ecd853749d7e4d4b926 |
| 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-d7d567ab2b304ecd853749d7e4d4b9262025-02-03T05:52:00ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/486191486191LaSalle-Type Theorems for General Nonlinear Stochastic Functional Differential Equations by Multiple Lyapunov FunctionsXueyan Zhao0Feiqi Deng1Xiaojing Zhong2Systems Engineering Institute, South China University of Technology, Guangzhou 510640, ChinaSystems Engineering Institute, South China University of Technology, Guangzhou 510640, ChinaSystems Engineering Institute, South China University of Technology, Guangzhou 510640, ChinaWe investigate LaSalle-type theorems for general nonlinear stochastic functional differential equations. With some preliminaries on lemmas and the derivation techniques, we establish three LaSalle-type theorems for the general nonlinear stochastic functional differential equations via multiple Lyapunov functions. For the typical special case with estimations involving |xt|p for the derivatives of the Lyapunov functions, a theorem is established as the corollary of the main theorem. At the end of the paper, an example is given to illustrate the usage of the method proposed and show the advantage of the results obtained.http://dx.doi.org/10.1155/2014/486191 |
| spellingShingle | Xueyan Zhao Feiqi Deng Xiaojing Zhong LaSalle-Type Theorems for General Nonlinear Stochastic Functional Differential Equations by Multiple Lyapunov Functions Abstract and Applied Analysis |
| title | LaSalle-Type Theorems for General Nonlinear Stochastic Functional Differential Equations by Multiple Lyapunov Functions |
| title_full | LaSalle-Type Theorems for General Nonlinear Stochastic Functional Differential Equations by Multiple Lyapunov Functions |
| title_fullStr | LaSalle-Type Theorems for General Nonlinear Stochastic Functional Differential Equations by Multiple Lyapunov Functions |
| title_full_unstemmed | LaSalle-Type Theorems for General Nonlinear Stochastic Functional Differential Equations by Multiple Lyapunov Functions |
| title_short | LaSalle-Type Theorems for General Nonlinear Stochastic Functional Differential Equations by Multiple Lyapunov Functions |
| title_sort | lasalle type theorems for general nonlinear stochastic functional differential equations by multiple lyapunov functions |
| url | http://dx.doi.org/10.1155/2014/486191 |
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