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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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Oscillation properties of $y^{n}+py=0$
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by Gary D. Jones PDF
Proc. Amer. Math. Soc. 78 (1980), 239-244 Request permission

Abstract:

The purpose of this paper is to give necessary and sufficient conditions for $(k,n - k)$ disconjugacy of ${y^n} + py = 0$. The results are then applied to give counterexamples to the following theorems of Nehari. If n is even and p is positive either all solutions of ${y^n} + py = 0$ oscillate or none do. If n is even and p is negative and ${y^n} + py = 0$ has an oscillatory solution then all positive nonoscillatory solutions are either strongly increasing or strongly decreasing.
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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 78 (1980), 239-244
  • MSC: Primary 34C10
  • DOI: https://doi.org/10.1090/S0002-9939-1980-0550504-3
  • MathSciNet review: 550504