Solutions of $(ry^{(n)})^{(n)} + qy = 0$ of class $\mathcal {L}_{p}[0, \infty )$
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- by Don Hinton PDF
- Proc. Amer. Math. Soc. 32 (1972), 134-138 Request permission
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 $\smallint _0^t|q{|^2}\;d\tau = O(t)$ as $t \to \infty$, then $m \leqq n$.References
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Additional Information
- © Copyright 1972 American Mathematical Society
- 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