Existence and controllability results for a new class of impulsive stochastic partial integro-differential inclusions with state-dependent delay
Existence and controllability results for a new class of impulsive stochastic partial integro-differential inclusions with state-dependent delay
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具有状态依赖时滞的新型脉冲随机部分积分微分包含的存在性和可控性结果
DOI：
10.1002/asjc.1413
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发表时间：
2017
影响因子：
2.4
通讯作者：
Xiumei Jia（贾秀梅）
中科院分区：
文献类型：
--
作者：
Zuomao Yan （闫作茂）;Xiumei Jia（贾秀梅）
本文研究了可分Hilbert空间中一类新的具有状态依赖时滞的脉冲随机偏积分微分包含。首先，利用随机分析理论、解析预解算子、闭算子的分数次幂和适当的不动点定理，证明了这类系统在-范数下的mild解和极值mild解的存在性。其次，我们建立了非瞬时脉冲受控随机偏积分微分包含的能控性。这些结果是在Lipschitz和Carathéodory混合条件下得到的。最后，通过一个例子说明了所得结果的应用.
In this paper, we study a new class of impulsive stochastic partial integro-differential inclusions with.state-dependent delay in separable Hilbert spaces. Firstly, by using stochastic analysis theory, analytic resolvent operators,.fractional powers of closed operators and suitable fixed point theorems, we prove the existence of mild and extremal.mild solutions for these systems in the -norm. Secondly, we establish the controllability of the controlled stochastic partial.integro-differential inclusions with not instantaneous impulses. The results are obtained under the mixed Lipschitz.and Carathéodory conditions. Finally, an example is provided to show the application of our results.