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Oscillation properties of the $ 2-2$ disconjugate fourth order selfadjoint differential equation


Author: Leo J. Schneider
Journal: Proc. Amer. Math. Soc. 28 (1971), 545-550
MSC: Primary 34.42
DOI: https://doi.org/10.1090/S0002-9939-1971-0281999-5
MathSciNet review: 0281999
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Abstract: This paper contains a proof that either all, or none, of the nontrivial solutions of the fourth order linear selfadjoint differential equation have an infinite number of zeros on a half line, provided that no nontrivial solution has more than one double zero on that half line.


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

  • [1] W. Leighton and Z. Nehari, On the oscillation of solutions of self-adjoint linear differential equations of the fourth order, Trans. Amer. Math. Soc. 89 (1958), 325-377. MR 21 #1429. MR 0102639 (21:1429)
  • [2] M. Morse, Introduction to analysis in the large, 2nd ed., Lectures, Institute for Advanced Study, Princeton, N.J., 1951; reprint, 1957. MR 16, 837. MR 0068140 (16:837c)
  • [3] G. Pólya, On the mean-value theorem corresponding to a given linear homogeneous differential equation, Trans. Amer. Math. Soc. 24 (1922), 312-324. MR 1501228
  • [4] A. Peterson, The distribution of zeros of extremal solutions of a fourth order differential equation for the $ n$-th conjugate point, J. Differential Equations 8 (1970), 502-511. MR 0269928 (42:4821)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0281999-5
Keywords: Conjugate point, disconjugacy, $ n{\text{ - }}n$ disconjugacy for $ n = 2$, Morse index, nonoscillatory solution, oscillatory solution, separation of zeros, self-adjoint differential equation of fourth order
Article copyright: © Copyright 1971 American Mathematical Society

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