On Boundary Value Problems for Hamiltonian Systems with Two Singular Points

A linear Hamiltonian system of differential equations is considered on an open interval $(a,b)$ where both a and b are singular points. A Green’s function is defined by a limit of such functions of regular problems. It is proved that solutions of the differential equations defined by the Green’s function satisfy Titchmarsh’s $\lambda $-dependent boundary conditions at the singular points. A formula linking the Titchmarsh–Weyl matrix m-coefficient to certain square integrable solutions is established for separated boundary conditions.