\(L^2\)-properties of solutions and ranks of radii of the limit matrix circles for nonselfadjoint systems of differential equations (Q871757)

This paper examines properties of the solutions of the differential equations \[ -(Py')'+Qy=0\quad\text{ and }\quad-(P^*y')'+Q^*y=0, \] where \(P\) and \(Q\) are complex \(n\times n\) matrix-valued functions defined on \([0,\infty )\) and the entries of \((P(x))^{-1}\) and \(Q(x)\) are locally integrable functions of \(x\). Results include bounds for the number of linearly independent solutions satisfying various conditions.