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Proceedings of the American Mathematical Society

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Schwarzian derivatives and zeros of solutions to second order linear differential equations


Authors: A. Hinkkanen and John Rossi
Journal: Proc. Amer. Math. Soc. 113 (1991), 741-746
MSC: Primary 34C10; Secondary 30D05, 34A20
DOI: https://doi.org/10.1090/S0002-9939-1991-1069689-5
MathSciNet review: 1069689
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Abstract: Let $ A$ be entire. Suppose that there exists an unbounded quasidisk $ D$ such that $ A$ is sufficiently small in $ D$. We prove that then any nontrivial solution to $ y'' + Ay = 0$ has at most one zero in $ D$. We show that if $ A = Q\exp P$ where $ P$ and $ Q$ are polynomials, one can usually take $ D$ to be an angle of opening $ \pi /n$ where $ n$ is the degree of $ P$.


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DOI: https://doi.org/10.1090/S0002-9939-1991-1069689-5
Article copyright: © Copyright 1991 American Mathematical Society

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