Abstract
In this paper, a class of nonlinear stochastic neutral differential equations with delays is investigated. By using the properties of \({\mathcal{M}}\) -matrix, a differential-difference inequality is established. Basing on the differential-difference inequality, we develop a \({\mathcal{L}}\) -operator-difference inequality such that it is effective for stochastic neutral differential equations. By using the \({\mathcal{L}}\) -operator-difference 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 p-stability 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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Long, S. Attracting and Invariant Sets of Nonlinear Stochastic Neutral Differential Equations with Delays. Results. Math. 63, 745–762 (2013). https://doi.org/10.1007/s00025-012-0231-4
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DOI: https://doi.org/10.1007/s00025-012-0231-4