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Disconjugacy Criteria for Self-Adjoint Differential Systems

机译：自伴微分系统的不一致性判据

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For self-adjoint matrix differential systems (1) Y' = G(x)Z, Z' = -F(x)Y, where G and F are nxn hermitian matrix functions, the author presents various criteria for disconjugacy. One of the basic results employs a generalization of a method used by Hille for real second order scalar differential equations, and involves the singular Riccati matrix integral equation. In several instances the obtained criteria generalize earlier results of Sternberg, especially in regard to removing conditions of non-singularity for the matrix function G. There are also obtained relationships between boundary problems involving (1) and a corresponding system with F and G interchanged. Applications are made to certain classes of differential equations of even order.

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