Existence, uniqueness and stability of stochastic neutral functional differential equations of Sobolev-type
Existence, uniqueness and stability of stochastic neutral functional differential equations of Sobolev-type
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DOI：
10.1109/chicc.2015.7259897
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发表时间：
2015-07
期刊：
影响因子：
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通讯作者：
Quanxin Zhu;Xuetao Yang
中科院分区：
文献类型：
--
作者：
Quanxin Zhu;Xuetao Yang
本文主要研究了一类带Poisson跳的Sobolev型随机中立型泛函微分方程。在两组不同的条件下，我们分别利用Leray-Schauder择一理论和Sadakovskii不动点定理证明了该问题的温和解的存在性。此外，我们还利用Bihari不等式证明了Osgood型唯一性。利用Gronwall不等式研究了系统的均方指数稳定性.最后，给出了两个例子来说明理论结果.
In this paper, we are mainly concerned with a class of stochastic neutral functional differential equations of Sobolev-type with Poisson jumps. Under two different sets of conditions, we establish the existence of the mild solution by applying the Leray-Schauder alternative theory and the Sadakovskii's fixed point theorem, respectively. Furthermore, we use the Bihari's inequality to prove the Osgood type uniqueness. Also, the mean square exponential stability is investigated by applying the gronwall inequality. Finally, two examples are given to illustrate the theory results.