Monodromy groups of parameterized linear differential equations with regular singularities.

We study the notion of regular singularities for parameterized complex ordinary linear differential systems, prove an analogue of the Schlesinger theorem for systems with regular singularities and solve both a parameterized version of the weak Riemann–Hilbert Problem and a special case of the inverse problem in parameterized Picard–Vessiot theory. [ABSTRACT FROM AUTHOR]