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Stability of second-order stochastic neutral partial functional differential equations driven by impulsive noises

Science China(Information Sciences) 2016年第11期59卷 117-127页

作者： Feng JIANG Hua YANG Yi SHEN School of Statistics and Mathematics Zhongnan University of Economics and Law School of Automation Huazhong University of Science and Technology School of Mathematics and Computer Science Wuhan Polytechnic University

This paper investigates the stability of second-order stochastic neutral partial functional differential equations driven by impulsive noises. Some sufficient conditions ensuring pth moment exponential stability of the second-order stochastic neutral partial functional differential equations driven by impulsive noises are obtained by establishing a new impulsive-integral inequality. These existing results are generalized and improved by the present study. Finally, an example is given to show the effectiveness of our results.

关键词： second-order stochastic neutral partial functional differential equations exponential stability impulsive noises sine family cosine family

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EXISTENCE OF SOLUTION AND APPROXIMATE CONTROLLABILITY OF A SECOND-ORDER NEUTRAL STOCHASTIC DIFFERENTIAL EQUATION WITH STATE DEPENDENT DELAY

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Acta Mathematica Scientia 2016年第5期36卷 1509-1523页

作者： Sanjukta DAS Dwijendra PANDEY N. SUKAVANAM Department of Mathematics Indian Institution of Technology Roorkee

This paper has two sections which deals with a second order stochastic neutral partial differential equation with state dependent delay. In the first section the existence and uniqueness of mild solution is obtained by use of measure of non-compactness. In the second section the conditions for approximate controllability are investigated for the distributed second order neutral stochastic differential system with respect to the approximate controllability of the corresponding linear system in a Hilbert space. Our method is an extension of co-author N. Sukavanam’s novel approach in [22]. Thereby, we remove the need to assume the invertibility of a controllability operator used by authors in [5], which fails to exist in infinite dimensional spaces if the associated semigroup is compact. Our approach also removes the need to check the invertibility of the controllability Gramian operator and associated limit condition used by the authors in [20], which are practically difficult to verify and apply. An example is provided to illustrate the presented theory.

关键词： approximate controllability cosine family state dependent delay neutral stochastic differential equation measure of noncompactness

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