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. © 2006 Elsevier Inc. All rights reserved.