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Proceedings of the American Mathematical Society

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Solutions of $ (ry^{(n)})^{(n)} + qy = 0$ of class $ \mathcal{L}_{p}[0, \infty)$


Author: Don Hinton
Journal: Proc. Amer. Math. Soc. 32 (1972), 134-138
MSC: Primary 34.40
DOI: https://doi.org/10.1090/S0002-9939-1972-0288348-8
MathSciNet review: 0288348
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Abstract: For a certain class of ordinary differential operators L, this paper determines the maximum number m of linearly independent solutions of class $ {\mathcal{L}_p}[0,\infty )$ of $ L(y) = 0$. For $ L(y) = {(r{y^{(n)}})^{(n)}} + qy$, and $ p = 2$, the principal result is that if $ \smallint _0^t\vert q{\vert^2}\;d\tau = O(t)$ as $ t \to \infty $, then $ m \leqq n$.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0288348-8
Keywords: Limit point, limit circle, $ {\mathcal{L}_p}$ solutions
Article copyright: © Copyright 1972 American Mathematical Society

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