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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Nonoscillation and eventual disconjugacy
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by Uri Elias PDF
Proc. Amer. Math. Soc. 66 (1977), 269-275 Request permission

Abstract:

If every solution of an nth order linear differential equation has only a finite number of zeros in $[0,\infty )$, it is not generally true that for sufficiently large $c,c > 0$, every solution has at most $n - 1$ zeros in $[c,\infty )$. Settling a known conjecture, we show that for any n, the above implication does hold for a special type of equation, ${L_n}y + p(x)y = 0$, where ${L_n}$ is an nth order disconjugate differential operator and $p(x)$ is a continuous function of a fixed sign.
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Additional Information
  • © Copyright 1977 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 66 (1977), 269-275
  • MSC: Primary 34C10
  • DOI: https://doi.org/10.1090/S0002-9939-1977-0460791-8
  • MathSciNet review: 0460791