Existence and uniqueness of solutions of semilinear stochastic infinite-dimensional differential systems with H-regular noise

Existence and uniqueness of approximate strong solutions of stochastic infinite-dimensional systemsdu=[A(t)u+B(t,u)]dt+G(t,u)dW,u(0,⋅)=u0∈H,t⩾0 with local Lipschitz-continuous, time-depending nonrandom operators A,BA,B and G acting on a separable Hilbert space H are studied. For this purpose, some monotonicity conditions on those operators and an existing U-series expansion of the space–time Wiener process W (U  -valued, U⊆HU⊆H, U   Hilbert space) with ∑n=1+∞αn2<+∞ belonging to the trace of related covariance operator Q of W   with local noise intensities αn2∈R1 as eigenvalues of Q are exploited.