Functional dependence and boundary-value problems with families of solutions

A linear Hamiltonian system Jy′ = (λA + B) y is considered on an open interval (a, b), where both a and b are singular. The system is assumed to be of limit point or limit circle type at the endpoints. A theory of boundary problems for such systems is developed. Explicit boundary conditions are given, resolvent operators constructed and unique solutions established. The results given extend to Hamiltonian systems a theory of singular boundary value problems due to M. H. Stone and K. Kodaira.