Summary: A review is given of the results obtained by the authors on the topic formulated in the title. New results are also presented: methods more general than those suggested earlier are described for constructing admissible boundary conditions at a singular point in the case of systems of first-order equations, and generalized systems of second-order equations with pole-type singularities are analysed, special attention being focused on the conditions of boundedness of the solutions at a singular point and to the emission-type conditions at infinity.