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

Abstract: 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 , in which the initial value belongs to the abstract space . We establish the existence and uniqueness of mild solutions for this kind of equations under some Carathéodory conditions by means of the successive approximation. The obtained result extends some well-known results. An example is proposed to illustrate the theory. [Copyright &y& Elsevier]