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Title of Journal: Results Math

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Abbravation: Results in Mathematics

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SP Birkhäuser Verlag Basel

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DOI

10.1016/0304-3959(83)90155-0

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1420-9012

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Attracting and Invariant Sets of Nonlinear Stochas

Authors: Shujun Long
Publish Date: 2012/02/04
Volume: 63, Issue: 3-4, Pages: 745-762
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Abstract

In this paper a class of nonlinear stochastic neutral differential equations with delays is investigated By using the properties of mathcalM matrix a differentialdifference inequality is established Basing on the differentialdifference inequality we develop a mathcalL operatordifference inequality such that it is effective for stochastic neutral differential equations By using the mathcalL operatordifference inequality we obtain the global attracting and invariant sets of nonlinear stochastic neutral differential equations with delays In addition we derive the sufficient condition ensuring the exponential pstability of the zero solution of nonlinear stochastic neutral differential equations with delays One example is presented to illustrate the effectiveness of our conclusion

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