Two-point boundary value problems associated with a system of generalized matrix differential equations (Q2761987)

The authors investigate existence and uniqueness of solutions to the generalized two-point boundary value problem NEWLINE\[NEWLINEdy=d[A]y+dg,\quad a\leq t\leq b,\quad My(a)+Ny(b)=0,NEWLINE\]NEWLINE where \(A\in BV^{n\times n}\), \(g\in BV^n\), \(y\in BV^n\), \(M,N\) are constant square matrices of order \(n\) and all scalars are assumed to be real. \(BV\), \(BV^n\), \(BV^{n\times n}\) are the Banach spaces of functions of bounded variation on \([a,b]\) taking values in \(\mathbb{R}\), \(\mathbb{R}^n\), \(\mathbb{R}^{n\times n}\), respectively. The results of the paper extend classical ones on two-point boundary value problems. Properties of the generalized Green's matrix are presented.