On differential equations in \(c\)-generalized functions (Q1390433)

Starting from the Cauchy problem for the linear differential equation \[ X'= B'(t)X+ F'(t),\quad t\in I, \] in the algebra of \(n\times n\) matrices over \(\mathbb{R}\), the authors are defining a very general notion of solutions to this problem in the class of Colombeau generalized functions. Properties of this type of solution and interesting examples are given. The classical Carathéodory notion of solution is included here.