Boundedness of solutions for singular Hamiltonian differential systems with applications to deficiency indices
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)].
scientific article; zbMATH DE number 5115289
scientific article