The conjugacy function
HTML articles powered by AMS MathViewer
- by Walter Leighton
- Proc. Amer. Math. Soc. 24 (1970), 820-823
- DOI: https://doi.org/10.1090/S0002-9939-1970-0257464-7
- PDF | Request permission
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.References
- 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 10.1007/BF02844035
- Walter Leighton, On self-adjoint differential equations of second order, J. London Math. Soc. 27 (1952), 37–47. MR 46506, DOI 10.1112/jlms/s1-27.1.37
- Walter Leighton, Principal quadratic functionals, Trans. Amer. Math. Soc. 67 (1949), 253–274. MR 34535, DOI 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 10.1090/S0002-9947-1955-0066570-8
Bibliographic Information
- © Copyright 1970 American Mathematical Society
- 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