Canonical forms and principal systems for general disconjugate equations
Author:
William F. Trench
Journal:
Trans. Amer. Math. Soc. 189 (1974), 319327
MSC:
Primary 34C10
MathSciNet review:
0330632
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Abstract: It is shown that the disconjugate equation (1) , a , where , and (2) , can be written in essentially unique canonical forms so that for . From this it follows easily that (1) has solutions which are positive in (a, b) near and satisfy for . Necessary and sufficient conditions are given for (1) to have solutions such that for . Using different methods, P. Hartman, A. Yu. Levin and D. Willett have investigated the existence of fundamental systems for (1) with these properties under assumptions which imply the stronger condition .
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DOI:
http://dx.doi.org/10.1090/S0002994719740330632X
PII:
S 00029947(1974)0330632X
Keywords:
Disconjugacy,
principal systems
Article copyright:
© Copyright 1974 American Mathematical Society
