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Proceedings of the American Mathematical Society

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

 

 

The nonequivalence of oscillation and nondisconjugacy


Author: G. B. Gustafson
Journal: Proc. Amer. Math. Soc. 25 (1970), 254-260
MSC: Primary 34.42
DOI: https://doi.org/10.1090/S0002-9939-1970-0284648-4
MathSciNet review: 0284648
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Abstract: A sufficient condition is given for all solutions of the adjoint of an $ n$th order linear differential equation to have an infinity of zeros; an example is presented which shows that for every integer $ n > 2$, there exists an $ n$th order equation, all of whose solutions have a finite number of zeros, but the adjoint has only solutions with an infinity of zeros. In addition, some open equations on conjugate points are answered.


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

  • [1] J. M. Dolan, Oscillatory behavior of solutions of linear ordinary differential equations of third order, Ph.D. Dissertation, University of Tennessee, Knoxville, Tenn., 1967.
  • [2] -, On the relationship between the oscillatory behavior of a linear third-order equation and its adjoint, J. Differential Equations (to appear).
  • [3] G. B. Gustafson, Conjugate point properties for $ n$th order linear differential equations, Ph.D. Dissertation, Arizona State University, Tempe, Ariz., 1968.
  • [4] Maurice Hanan, Oscillation criteria for third-order linear differential equations., Pacific J. Math. 11 (1961), 919–944. MR 0145160
  • [5] Philip Hartman, Ordinary differential equations, John Wiley & Sons, Inc., New York-London-Sydney, 1964. MR 0171038

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0284648-4
Keywords: $ n$th conjugate point, oscillatory, nonoscillatory, strongly oscillatory, disconjugate, zeros counted according to multiplicity
Article copyright: © Copyright 1970 American Mathematical Society