时滞依赖于状态的脉冲中立型随机发展积分微分方程温和解的存在性

Existence of Mild Solutions for Impulsive Neutral Stochastic Evolution Integro-differential Equations with State-dependent Delay

研究一类时滞依赖于状态的脉冲中立型随机发展积分微分方程温和解的存在性,基于不动点定理、预解算子理论和相空间理论,借助算子半群方法和随机分析,在合适的条件下获得了上述方程温和解存在的一般性定理。最后,以随机热传导方程为实例论证了结论的有效性。

The existence of mild solutions for a class of impulsive neutral stochastic evolution integro-differential equations with state-dependent delay was studied. Based on the fixed point theorem, resolvent operator theory and phase space theory, a general theorem of the existence result was obtained under the appropriate conditions by means of the operator semigroup method and stochastic analysis technique. Finally, an example of stochastic heat conduction equation was given to illustrate the validity of the main results.