Constructive investigation methods for multi-point boundary value problems (Q1311173)

The paper deals with the multipoint boundary value problem (1) \({dy \over dx} =A(x)y+f(x)\), (2) \(\sum^ m_{q=1} F_ q(y(x_ q))=\alpha\), \(q=1,\dots,m\), \(1 \leq m \leq n\), where \(a=x_ 1<x_ 2<\cdots<x_ m=b\), \(a,b \in \mathbb{R}\), \(A\), \(f\) are continuous on \([a,b]\), \(F_ q\) are constant \(n \times n\) matrices, \(\alpha \in \mathbb{R}\). Under appropriate assumptions the author shows a representation of the unique solution of problem (1), (2) in terms of the fundamental matrix for (1), (2). He also transforms problem (1), (2) onto a special integral equation. Some applications are shown as well.