Boundedness of solutions for singular Hamiltonian differential systems with applications to deficiency indices (Q858640)

Using special properties of Hamiltonian differential systems, the author obtains boundedness estimates of solutions for the higher-dimensional Hamiltonian differential system \[ Jy'(t)=[\lambda W(t)+P(t)]y(t) \] over the interval \(R^+=[0,+\infty)\), where \(\lambda\) is a complex parameter, \(J=\left( \begin{matrix} 0, & -I\\ I, & 0 \end{matrix} \right)\), \(I\) is the \(n\times n\) identity matrix and \(P^\ast(t)=P(t)\), \(W^\ast(t)=W(t)\geq 0\) are locally integrable \(2n\times 2n\) complex-valued Hermitean matrices (\(W(t)\) is nonnegative definite). As corollaries limit-circle criteria are established, one special case of which improves the results in [\textit{B. J. Harris}, ``Limit-circle criteria for second order differential expressions'', Q. J. Math., Oxf. II. Ser. 35, 415--427 (1984; Zbl 0558.34030)].