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Proceedings of the American Mathematical Society

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

 

 

Simple zeros of solutions of $ n{\rm th}$-order linear differential equations


Author: W. J. Kim
Journal: Proc. Amer. Math. Soc. 28 (1971), 557-561
MSC: Primary 34.42
MathSciNet review: 0274861
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Abstract: Let the $ n$th-order linear differential equation $ Ly = 0$ have a nontrivial solution with $ n$ zeros (counting multiplicities) on an interval $ [\alpha ,\beta ]$. A condition under which $ Ly = 0$ has a solution with $ n$ simple zeros on $ [\alpha ,\beta ]$ is established.

Also, a new proof is given for a known result concerning an interval of the type $ [\alpha ,\beta )$.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0274861-5
Keywords: Existence of solutions with $ n$ simple zeros, linear equations, ordinary, $ n$th-order, real-valued continuous coefficients
Article copyright: © Copyright 1971 American Mathematical Society