Fixed Points and Asymptotic Properties of Neutral Stochastic Delay Differential Equations

This paper discusses a linear neutral stochastic differential equation with variable delays. By using fixed point theory, the necessary and sufficient conditions are given to ensure that the trivial solution to such an equation is pth moment asymptotically stable. These conditions do not require the boundedness of delays, nor derivation of delays. An example was also given for illustration.

Krasnoselskii不动点与中立型多变时滞随机动力系统的指数p稳定性

探讨了一类中立型多变时滞随机动力系统,并通过Krasnoselskii不动点方法,给出了该系统零解指数p稳定的条件;同时对所得结果进行了严格的证明,形成了中立型多变时滞随机动力系统零解指数p稳定性定理。本文首次采用Krasnoselskii不动点方法研究了一类中立型多变时滞随机动力系统零解的指数p稳定性,所得结果改进和推广了已有文献中的结论;并且根据多变时滞随机动力系统时滞τ_i(t)和δ_i(t)的特点,分别引入对应的函数h_i(s),i=1,2,L,n来构造算子,相比已有文献中的方法更加灵活实用。

Schauder不动点与中立型随机动力系统的稳定性

文章利用Schauder不动点方法研究了一类中立型随机动力系统,并给出了该系统零解指数均方稳定的条件。在研究中立型多变时滞随机动力系统的稳定性时,大多数专家采用的都是Lyapunov直接法和Banach不动点方法,Schauder不动点方法还很少见。文章在证明过程中,根据系统多变时滞的特点,配对引入对应的函数来构造算子,相比以往的研究更加灵活。文章第一次尝试通过实例对Lyapunov直接法、Banach不动点方法和Schauder不动点方法在研究随机动力系统稳定性上的优劣进行了比较分析。文章的结果改进和推广了相关文献的结论,详见实例。

Oscillation of Second-order Nonlinear Dynamic Equation on Time Scales

The oscillation for a class of second order nonlinear variable delay dynamic equation on time scales with nonlinear neutral term and damping term was discussed in this article. By using the generalized Riccati technique, integral averaging technique and the time scales theory, some new sufficient conditions for oscillation of the equation are proposed. These results generalize and extend many known results for second order dynamic equations. Some examples are given to illustrate the main results of this article.

中立多变时滞Volterra型随机动力系统的稳定性

探讨了一类非线性随机积分微分动力系统,并通过Banach不动点方法,给出了该系统零解均方渐近稳定的充要条件,形成了中立多变时滞Volterra型随机积分微分动力系统零解均方渐近稳定性定理.与前人的研究方法不同,该文根据多变时滞随机动力系统各时滞的特点,灵活构造算子,相比以往文献的方法更加灵活实用。文章的结论一定程度上改进和发展了相关研究论文的结果。另外,文章所得结论补充并推广了不动点方法在研究非线性中立多变时滞Volterra型随机积分微分动力系统零解稳定性方面的成果.