一类随机发展方程mild解的存在唯一性

Existence and Uniqueness of Mild Solutions for a Class of Stochastic Evolution Equations

运用分数幂算子、逐次逼近法及不动点定理研究Hilbert空间中的非自治中立型随机时滞发展方程mild解的存在唯一性。考虑到无界线性算子族A(t)可以在Hilbert空间中生成唯一的线性发展系统{U(t,s):0≤s≤t≤T},且方程中的非线性项不满足Lipschitz条件,使得所讨论的方程作为数学模型更符合实际应用。

In this paper,we mainly use fractional power operator,successive approximation method and fixed point theorem to study the existence and uniqueness of mild solutions for nonautonomous neutral stochastic delay evolution equation in Hilbert spaces.Considering that the unbounded family of linear operators A(t)can generate a unique linear evolution system{U(t,s):0≤s≤t≤T}in Hilbert spaces,and the nonlinear term in the equation does not satisfy Lipschitz conditions,the equation is more suitable for practical application as a mathematical model.