Conjugate Points of Singular Quadratic Functionals for N Dependent Variables

Authors

John O. Chellevold, Wartburg CollegeFollow

Document Type

Research

Abstract

Morse and Leighton (Singular quadratic functionals. Transactions of the American Mathematical Society, volume 40 (1936) pp. 252-286) gave a systematic approach to the problem of minimizing a singular quadratic functional for one dependent variable considering integrands of the type f (x, y, y') = r(x) y'² + 2q (x) y y' + p (x) y² where r, q, and p are single-valued continuous functions of the real variable x on the interval (0, d)⁽²⁾ and r is positive. They defined first conjugate point of the singular point x = 0. They defined minimum limit of a functional and determined conditions under which [o, b] would afford such a limit to a functional among several classes of comparison curves.

Publication Date

1952

Journal Title

Proceedings of the Iowa Academy of Science

Volume

59

Issue

1

First Page

331

Last Page

337

Copyright

©1952 Iowa Academy of Science, Inc.

Language

en

File Format

application/pdf

Recommended Citation

Chellevold, John O. (1952) "Conjugate Points of Singular Quadratic Functionals for N Dependent Variables," Proceedings of the Iowa Academy of Science, 59(1), 331-337.
Available at: https://scholarworks.uni.edu/pias/vol59/iss1/40