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Article Contents

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

• 1Corresponding author

The research was supported in part by the National Natural Science Foundations of China (Grant Nos. 1161101211 and 61873320), and the Royal Society and the Newton Fund (NA160317, Royal Society-Newton Advanced Fellowship)

• 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.

Mathematics Subject Classification: Primary: 34K50, 60H10; Secondary: 34D45, 37C75.

 Citation:

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