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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

© Copyright 1952 by the Iowa Academy of Science, Inc.

Language

EN

File Format

application/pdf

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