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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Lower bounds to the zeros of solutions of $y^{”}+ p(x)y=0$


Author: A. S. Galbraith
Journal: Proc. Amer. Math. Soc. 26 (1970), 111-116
MSC: Primary 34.42
DOI: https://doi.org/10.1090/S0002-9939-1970-0265679-7
MathSciNet review: 0265679
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Abstract | References | Similar Articles | Additional Information

Abstract: If $p(x)$ is nonnegative, monotonic and concave, no solution of $y'' + p(x)y = 0$ has more than $n + 1$ zeros in the interval $(a,b)$ defined by \[ (b - a)\int _a^b {p(x)dx = {n^2}{\pi ^2}.} \] This is proved by showing that, if $y’(a) = 0$, the $n$th succeeding zero of $y’(x)$ will not precede $b$.


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Keywords: Linear differential equations, lower bounds to zeros, estimates of characteristic values, number of zeros in an interval
Article copyright: © Copyright 1970 American Mathematical Society