Approximate controllability of a class of second order stochastic evolution equations with infinite delay(一类具有无穷时滞的二阶随机发展方程的近似可控性)

This paper presents a study on existence and approximate controllability of the mild solution of a class of second order stochastic evolution equations with infinite delay in Hilbert space. It proves the existence of the mild solution of the studied problem by using the cosine family theory, Hölder inequality, stochastic analysis theory and Mönch fixed point theorem. At the same time, the iterative technique is used to construct the convergent sequence, meanwhile the sufficient condition for the approximate controllability of the problem is obtained by combining the range condition.研究了Hilbert空间中一类具有无穷时滞的二阶随机发展方程。利用余弦族理论、Hölder不等式、随机分析理论和Mönch不动点定理，证明了该方程mild解的存在性；并运用迭代技术构造收敛序列，结合值域型条件，获得了该方程近似可控的充分条件。