Basic properties of some differential-algebraic equations (Q1117078)

The solvability of the equation \(Ax'+Bx=q\) with a regular modified local matrix pencil of higher index is considered. It is shown how to formulate initial conditions properly and that the initial value problems lead to operators with unbounded inverses. The close relationship of the matrix pencils needed in the investigation and of the related chains of the reduction methods is pointed out.