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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The conjugacy function


Author: Walter Leighton
Journal: Proc. Amer. Math. Soc. 24 (1970), 820-823
MSC: Primary 34.42
DOI: https://doi.org/10.1090/S0002-9939-1970-0257464-7
MathSciNet review: 0257464
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Abstract: The conjugacy function $ \delta (x)$ of the differential equation $ y'' + p(x)y = 0$ is defined as the distance from a point $ x$ to its first conjugate point. Conditions that $ \delta (x)$ be convex or concave are given, as well as conditions that $ \delta (x)$ be an increasing or decreasing function. The lemma provides a novel type of comparison theorem.


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DOI: https://doi.org/10.1090/S0002-9939-1970-0257464-7
Keywords: Second-order linear differential equation, conjugate point, conjugacy function, comparison theorem
Article copyright: © Copyright 1970 American Mathematical Society