A note on the second-order non-autonomous neutral stochastic evolution equations with infinite delay under Caratheodory conditions

作者：Ren, Yong^*; Hou, Tingting; Sakthivel, R.; Cheng, Xing

来源：Applied Mathematics and Computation, 2014, 232: 658-665.

DOI：10.1016/j.amc.2014.01.091

• Second-order neutral stochastic evolution equation
• Non-autonomous
• Infinite delay
• Caratheodory condition

In this note, we aim to study a class of second-order non-autonomous neutral stochastic evolution equations with infinite delay driven by a standard cylindrical Wiener process and an independent cylindrical fractional Brownian motion with Hurst parameter H is an element of (1/2,1), in which the initial value belongs to the abstract space B. We establish the existence and uniqueness of mild solutions for this kind of equations under some Caratheodory conditions by means of the successive approximation. The obtained result extends some well-known results. An example is proposed to illustrate the theory.

• 出版日期2014-4-1
• 单位安徽师范大学