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Proceedings of the American Mathematical Society

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

 

 

A sufficient condition for eventual disconjugacy


Author: William F. Trench
Journal: Proc. Amer. Math. Soc. 52 (1975), 139-146
MSC: Primary 34C10
DOI: https://doi.org/10.1090/S0002-9939-1975-0377189-1
MathSciNet review: 0377189
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Abstract: It is known that the scalar equation $ {y^{(n)}} + {p_1}(t){y^{(n - 1)}} + \cdots + {p_n}(t)y = 0,t > 0,n > 1$, is eventually disconjugate if $ {p_1}, \ldots ,{p_n}\epsilon C[0,\infty )$ and $ \int {^\infty \vert{p_i}(t)\vert{t^{i - 1}}dt < \infty ,1 \leqslant i \leqslant n} $. This paper presents a weaker integral condition which also implies that the given equation is eventually disconjugate.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0377189-1
Keywords: Eventually disconjugate, linear
Article copyright: © Copyright 1975 American Mathematical Society