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Proceedings of the American Mathematical Society

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



Nonoscillation and eventual disconjugacy

Author: Uri Elias
Journal: Proc. Amer. Math. Soc. 66 (1977), 269-275
MSC: Primary 34C10
MathSciNet review: 0460791
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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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Keywords: Nonoscillation, eventual disconjugacy, conjugate points
Article copyright: © Copyright 1977 American Mathematical Society