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

Wang, Ya and Wu, Fuke and Mao, Xuerong and Zhu, Enwen (2020) Advances in the LaSalle-type theorems for stochastic functional differential equations with infinite delay. Discrete and Continuous Dynamical Systems - Series B, 25 (1). pp. 287-300. ISSN 1531-3492 (https://doi.org/10.3934/dcdsb.2019182)

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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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