  This note is a development of our two previous papers, arXiv:1212.3392v1 and
1306.3660v1.
  The fundamental question is whether there exists a Galois theory, in which
the Galois group is a quantum group.
  For a linear equations with respect to a Hopf algebra, we arrived at a final
form if the base field consists of constants. In this case, we have
non-commutative Picard-Vessiot rings and asymmetric Tannaka theory.
  For non-linear equations there are examples that might make us optimistic.
