Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • [1] T. J. I'a. Bromwich, An introduction to the theory of infinite series, Macmillan, New York and London, 1955.
  • [2] W. A. Coppel, Stability and asymptotic behavior of differential equations, Heath, Boston, Mass., 1955. MR 0190463 (32:7875)
  • [3] G. Pólya, On the mean-value theorem corresponding to a given linear homogeneous differential equation, Trans. Amer. Math. Soc. 24 (1924), 312-324. MR 1501228
  • [4] D. Willett, Disconjugacy tests for singular linear differential equations, SIAM. J. Math. Anal. 2 (1971), 536-545. MR 46 #3904. MR 0304772 (46:3904)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34C10

Retrieve articles in all journals with MSC: 34C10


Additional Information

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

American Mathematical Society