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Proceedings of the American Mathematical Society

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

 

 

Lower bounds to the zeros of solutions of $ y\sp{''}+ 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: 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

$\displaystyle (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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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0265679-7
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