On the parameterized differential inverse Galois problem over k((t))(x)

In this article, we consider the inverse Galois problem for parameterized differential equations over k((t))(x) with k any field of characteristic zero and use the method of patching over fields due to Harbater and Hartmann. We show that every connected semisimple k((t))-split linear algebraic group is a parameterized differential Galois group over k((t))(x).