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

Ridenhour, Jerry R.

doi:10.1090/S0002-9939-1974-0330630-1

On $(n, n)$-zeros of solutions of linear differential equations of order $2n$
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by Jerry R. Ridenhour PDF

Proc. Amer. Math. Soc. 44 (1974), 135-140 Request permission

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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Explicit conditions for the factorization of $n$th order linear differential operators

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