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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

On the oscillation of differential equations with an oscillatory coefficient


Authors: B. J. Harris and Q. Kong
Journal: Trans. Amer. Math. Soc. 347 (1995), 1831-1839
MSC: Primary 34C10
DOI: https://doi.org/10.1090/S0002-9947-1995-1283552-4
MathSciNet review: 1283552
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Abstract | References | Similar Articles | Additional Information

Abstract: We derive lower bounds for the distance between consecutive zeros of solutions of

$\displaystyle ( * )\quad y'' + q(t)y = 0$

when $ q$ takes both positive and negative values. We apply our results to the limit point/limit circle classifications of $ ( * )$.

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

  • [1] W. A. Coppe, Disconjugacy, Springer, Berlin, Heidelberg, and New York, 1970. MR 0460785 (57:778)
  • [2] B. J. Harris, On an inequality of Lyapunov for disfocality, J. Math. Anal. Appl. 140 (1990), 495-500. MR 1043117 (91h:34041)
  • [3] P. Hartman. Ordinary differential equations, 2nd ed., Birkhäuser, Boston, Basel, and Stuttgart, 1982. MR 658490 (83e:34002)
  • [4] M. K. Kwong, On Lyapunov's inequality for disfocality, J. Math. Anal. Appl. 83 (1981), 486494. MR 641347 (83i:34030)
  • [5] -, On certain Riccati integral equations and second order linear oscillation, J. Math. Anal. Appl. 85 (1982), 315-330. MR 649178 (83f:34035)
  • [6] W. T. Patula and J. S. W. Wong, An $ {L^p}$ analogue of the Weyl alternative Math. Ann. 197 (1972), 9-28. MR 0299865 (45:8913)
  • [7] Jurang Yan, On the distance between zeros and the limit point problem, Proc. Amer. Math. Soc. 107 (1989), 971-975. MR 984825 (90d:34067)

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DOI: https://doi.org/10.1090/S0002-9947-1995-1283552-4
Article copyright: © Copyright 1995 American Mathematical Society

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