An abstract doubly nonlinear equation with a measure as initial value

The solvability of the abstract implicit nonlinear nonautonomous differential equation (A(t)u′(t))+B(t)u(t)+C(t)u(t)∋f(t) will be investigated in the case of a measure as an initial value. It will be shown that this problem has a solution if the inner product of A(t)x and B(t)x+C(t)x is bounded below.