Conjugate points of vector-matrix differential equations

Author:
Roger T. Lewis

Journal:
Trans. Amer. Math. Soc. **231** (1977), 167-178

MSC:
Primary 34C10

DOI:
https://doi.org/10.1090/S0002-9947-1977-0442364-0

MathSciNet review:
0442364

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Abstract: The system of equations

*y*is a vector, and is positive definite.

It is shown that the well-known quadratic functional criterion for existence of conjugate points for this system can be further utilized to extend results of the associated scalar equation to the vector-matrix case, and in some cases the scalar results are also improved. The existence and nonexistence criteria for conjugate points of this system are stated in terms of integral conditions on the eigenvalues or norms of the coefficient matrices.

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DOI:
https://doi.org/10.1090/S0002-9947-1977-0442364-0

Article copyright:
© Copyright 1977
American Mathematical Society