Non-limit-circle criteria for singular Hamiltonian differential systems
The paper deals with the singular Hamiltonian system \[ Jy^{\prime }(t)=[\lambda P(t)+Q(t)]y(t)\tag{1} \] over the interval \([0,+\infty ),\) where \(\lambda \) is a complex parameter, \(J \) is the symplectic matrix, \(P,Q\) are locally integrable complex-valued Hermitian matrices, with \(P\) nonnegative definite. The main focus of the paper is to present sufficient conditions, depending on \(P\) and \(Q,\) for the semi-degenerate system (1) to be in the non-limit-circle case.
scientific article; zbMATH DE number 2162025
scientific article