Advances in the LaSalle-type theorems for stochastic functional differential equations with infinite delay

Ya Wang, Fuke Wu, Xuerong Mao, Enwen Zhu

Research output: Contribution to journalArticle

Abstract

This paper considers stochastic functional differential equations (SFDEs) with infinite delay. The main aim is to establish the LaSalle-type theorems to locate limit sets for this class of SFDEs. In comparison with the existing results, this paper gives more general results under the weaker conditions imposed on the Lyapunov function. These results can be used to discuss the asymptotic stability and asymptotic boundedness for SFDEs with infinite delay. In the end, two examples will be given to illustrate applications of our new results established.
LanguageEnglish
Number of pages14
JournalDiscrete and Continuous Dynamical Systems - Series B
Publication statusAccepted/In press - 18 Mar 2019

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Stochastic Functional Differential Equations
Infinite Delay
Differential equations
Theorem
Lyapunov functions
Asymptotic stability
Limit Set
Asymptotic Stability
Lyapunov Function
Boundedness

Keywords

  • stochastic functional differential equations
  • SFDEs
  • infinite delay
  • LaSalle-type theorems

Cite this

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abstract = "This paper considers stochastic functional differential equations (SFDEs) with infinite delay. The main aim is to establish the LaSalle-type theorems to locate limit sets for this class of SFDEs. In comparison with the existing results, this paper gives more general results under the weaker conditions imposed on the Lyapunov function. These results can be used to discuss the asymptotic stability and asymptotic boundedness for SFDEs with infinite delay. In the end, two examples will be given to illustrate applications of our new results established.",
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AB - This paper considers stochastic functional differential equations (SFDEs) with infinite delay. The main aim is to establish the LaSalle-type theorems to locate limit sets for this class of SFDEs. In comparison with the existing results, this paper gives more general results under the weaker conditions imposed on the Lyapunov function. These results can be used to discuss the asymptotic stability and asymptotic boundedness for SFDEs with infinite delay. In the end, two examples will be given to illustrate applications of our new results established.

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KW - LaSalle-type theorems

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