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Proceedings of the American Mathematical Society

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Oscillation properties of $ y\sp{n}+py=0$


Author: Gary D. Jones
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
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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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DOI: https://doi.org/10.1090/S0002-9939-1980-0550504-3
Keywords: Differential equations, disconjugate, oscillation
Article copyright: © Copyright 1980 American Mathematical Society

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