Stochastic delay differential equations in a Hilbert space driven by fractional Brownian motion

In this paper, we prove an existence and uniqueness result of mild solution for a stochastic delay differential equation in a Hilbert space driven by a fractional Brownian motion with the Hurst parameter H>1∕2 and with a non-deterministic diffusion coefficient. We also prove under a sufficient condition that the law of the norm of the solution admits a density with respect to Lebesgue measure on R.