A supplement to oscillation and comparison theory for hermitian differential systems

For hermitian differential systems there is presented a characterization of a conjoined family of solutions (U; V) for which U is nonsingular between a pair of mutually conjugate points, or on an interval contiguous to a focal point. The general results are obtained without any assumption of normality of the system. For a class of systems which are direct generalizations of the canonical form of nonsingular accessory systems associated with a simple integral variational problem with no differential equation restraints, there is established a special comparison theorem involving a pointwise monotoneity property of the related integrand functions. The final section is devoted to a special result for systems consisting of a pair of scalar equations with real coefficients, which in case the coefficient functions are continuous provides the result of the basic theorem of a recent paper [Applicable Analysis 2 (1972), 355–376] by J. B. Diaz and J. R. McLaughlin.