Generalized Green's functions for higher order boundary value matrix differential systems (Q1196608)

The authors give existence conditions for the solution of the problem \(X^{(p)}+A_{p-1}X^{(p-1)}+\cdots+A_ 0X=f(t)\), \(0\leq t\leq b\), \(\sum^ p_{j=1}[E_{ij}X^{(j-1)}(0)+F_{ij}X^{(j-1)}(b)]=r_ i\), \(1\leq i\leq q\), where \(f(t)\), \(X(t)\), \(r_ i\) are matrices in \(C^{n\times m}\); \(A_ k\), \(E_{ij}\), \(F_{ij}\) are matrices in \(C^{n\times n}\), \(0\leq k\leq p-1\), as well as an explicit expression of a solution of the problem in terms of a generalized Green's matrix function without considering an extended first order problem and without the restriction of the existence of solutions of the associated algebraic matrix equation \(Z^ p+A_{p-1}Z^{p-1}+\cdots+A_ 0Z=0\). An illustrative example is given.