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 | References | Similar Articles | Additional Information
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.
- Ruth Lind Potter, On self-adjoint differential equations of second order, Pacific J. Math. 3 (1953), 467–491. MR 56156
- A. Samanich Skidmore and Walter Leighton, On the oscillation of solutions of a second-order linear differential equation, Rend. Circ. Mat. Palermo (2) 14 (1965), 327–334. MR 214857, DOI https://doi.org/10.1007/BF02844035
- Walter Leighton, On self-adjoint differential equations of second order, J. London Math. Soc. 27 (1952), 37–47. MR 46506, DOI https://doi.org/10.1112/jlms/s1-27.1.37
- Walter Leighton, Principal quadratic functionals, Trans. Amer. Math. Soc. 67 (1949), 253–274. MR 34535, DOI https://doi.org/10.1090/S0002-9947-1949-0034535-5
- Walter Leighton and Allan D. Martin, Quadratic functionals with a singular end point, Trans. Amer. Math. Soc. 78 (1955), 98–128. MR 66570, DOI https://doi.org/10.1090/S0002-9947-1955-0066570-8
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Additional Information
Keywords:
Second-order linear differential equation,
conjugate point,
conjugacy function,
comparison theorem
Article copyright:
© Copyright 1970
American Mathematical Society