Limit-point criterion for singular linear Dirac differential systems (Q2485507)

Three new limit point criteria are given for the \((2n,2n)\) Hamiltonian differential system \[ Jy'(t)= (\lambda P(t)+ Q(t))y(t), \quad 0\leq t<\infty, \qquad J= \left[\begin{matrix} 0 & -I\\ I & 0\end{matrix}\right], \] where \(I\) is the \((n,n)\) identity matrix and \(P(t)\), \(Q(t)\) are locally integrable complex matrices \(P^*= P> 0\), \(Q= Q^*\). The criteria extend ones by A. M. Krall, D. B. Hinton, J. K. Shaw. The first has been derived by \textit{M. Lesch} and \textit{M. Malumud} by a different method [J. Differ. Equations 189, No. 2, 556--615 (2003; Zbl 1016.37026)]. The second implies that the limit point is a strong limit point. The third extends the Levinson criterion to the Dirac type of differential operator.