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Proceedings of the American Mathematical Society

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



On the extremal solutions of $ n$th-order linear differential equations

Author: W. J. Kim
Journal: Proc. Amer. Math. Soc. 33 (1972), 62-68
MSC: Primary 34C10
MathSciNet review: 0294780
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Abstract: Distribution of zeros of extremal solutions of linear nth-order differential equations is discussed. Existence and nonexistence of extremal solutions with certain zero distributions are established. For instance, it is proved that every extremal solution for $ [\alpha, {\eta _1}(\alpha )]$ of the equation $ {y^{(n)}} + {p_{n - 1}}{y^{(n - 1)}} + \cdots + {p_0}y = 0$ has a zero of order 2 at $ {\eta _1}(\alpha )$ and has no more than $ n - 2$ zeros on $ [\alpha, {\eta _1}(\alpha ))\;{\text{if}}\;{p_i} \leqq 0,i = 0,1, \cdots, n - 2$.

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Keywords: nth-order linear equations with real-valued continuous coefficients, zero distribution of extremal solutions, existence and nonexistence
Article copyright: © Copyright 1972 American Mathematical Society