Explicit solution of higher order boundary value regular differential systems avoiding the increase of the problem dimension

Abstract

In this paper we obtain existence conditions and an expression of the general solution of higher order regular boundary value differential systems. The approach is based on the concept of co-solution of certain algebraic matrix equation and unlike to the classical approach we avoid the increase of the problem dimension derived from the consideration of an extended first order system.

Keywords:

• Regular differential systems
• boundary value problem
• Drazin inverse
• matrix equation

AMS:

• 34B10
• 34A09
• 34A30
• 15A22
• 65F20