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Proceedings of the American Mathematical Society

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On $ (n,\,n)$-zeros of solutions of linear differential equations of order $ 2n$


Author: Jerry R. Ridenhour
Journal: Proc. Amer. Math. Soc. 44 (1974), 135-140
MSC: Primary 34C10
DOI: https://doi.org/10.1090/S0002-9939-1974-0330630-1
MathSciNet review: 0330630
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Abstract: Sufficient conditions on the coefficients $ {p_{2n}},{p_{2n - 1}}, \cdots ,{p_0}$ are given which guarantee that no nontrivial solution of $ {p_{2n}}{y^{(2n)}} + {p_{2n - 1}}{y^{(2n - 1)}} + \cdots + {p_0}y = 0$ has two distinct zeros each of order at least $ n$. These conditions are in the form of $ n$ inequalities which are satisfied by linear combinations of the coefficients and their derivatives.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0330630-1
Keywords: Linear differential equations of order $ 2n$, $ (n,n)$-zeros of solutions, auxiliary function, inequalities satisfied by coefficients, Wronskian matrix, factorization of differential operators
Article copyright: © Copyright 1974 American Mathematical Society