  This paper is on the inverse parameterized differential Galois problem. We
show that surprisingly many groups do not occur as parameterized differential
Galois groups over K(x) even when K is algebraically closed. We then combine
the method of patching over fields with a suitable version of Galois descent to
prove that certain groups do occur as parameterized differential Galois groups
over k((t))(x). This class includes linear differential algebraic groups that
are generated by finitely many unipotent elements and also semisimple connected
linear algebraic groups.
