On the two-point boundary-value problem for the Riccati matrix differential equation (Q1767421)

The authors study a two-point boundary-value problem for the Riccati matrix differential equation of the form \[ {dX\over dt}= A(t) X+ XB(t)+ XQ(t)X+ F(t), \] where \(A,B,Q,F\in C(I,\mathbb{R}^{n\times m})\), \(I= [0,\omega]\), \(\omega> 0\), and with the boundary conditions \(MX(0)= NX(\omega)= 0\), where \(M\) and \(N\) are real \(n\times n\)-matrices. They find conditions on the matrices and the matrix functions involved guaranteeing a unique solution to this problem.