Approximate solutions for a class of stochastic evolution equations with variable delays. II
Approximate solutions for a class of stochastic evolution equations with variable delays. II
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DOI：
10.1080/01630569408816550
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发表时间：
1991
影响因子：
1.2
通讯作者：
X. Mao
中科院分区：
文献类型：
--
作者：
X. Mao
本文是我们在文献[9]中建立的Hilbert空间中具有变时滞的随机发展方程的Caratheodory近似解的继续，当f和g是Lipschitz时.在本文中，我们将显示相同的近似解的延迟方程，但系数f和g被假定为弱于Lipschitz连续。Caratheodory逼近的收敛性证明是建立时滞方程解的存在性和唯一性的另一种方法
This is a continuation of our previous paper [9] where we established the Caratheodory approximate solution for a stochastic evolution equation with variable delay in Hilbert space of the form when the coefficients f and g were Lipschitz. In this paper we shall show the same approximate solution for the delay equation but the coefficients f and g are supposed to be weaker than Lipschitz continuity. The proof of the convergence of the Caratheodory approximation represents an alternative to the procedure for establishing the existence and uniqueness of the solution to the delay equation