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Attracting and Invariant Sets of Nonlinear Stochastic Neutral Differential Equations with Delays

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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 \({\mathcal{M}}\) -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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  1. College of Mathematics and Information Science, Leshan Normal University, Leshan, 614004, People’s Republic of China

    Shujun Long

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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

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