On the uniqueness of maximal immediate extensions of valued differential fields

So far there exist just a few results about the uniqueness of maximal immediate valued differential field extensions and about the relationship between differential-algebraic maximality and differential-henselianity; see [1, Chapter 7]. We remove here the assumption of monotonicity in these results but replace it with the assumption that the value group is the union of its convex subgroups of finite (archimedean) rank. We also show the existence and uniqueness of differential-henselizations of asymptotic fields with such a value group.