A disconjugacy criterion for linear scalar differential operators

Author:
James S. Muldowney

Journal:
Proc. Amer. Math. Soc. **65** (1977), 93-96

MSC:
Primary 34C10

DOI:
https://doi.org/10.1090/S0002-9939-1977-0442367-1

MathSciNet review:
0442367

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Abstract: It is shown that if a linear scalar differential operator is not disconjugate on an interval then each member of a certain family of first order vector differential equations has an oscillatory solution. Thus any condition which guarantees the nonoscillation of a member of the family is a disconjugacy criterion for the scalar operator. The form of the vector systems is convenient for the use of nonoscillation conditions developed by Nehari, Schwarz and Friedland.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1977-0442367-1

Keywords:
Disconjugacy,
nonoscillation

Article copyright:
© Copyright 1977
American Mathematical Society