The nonequivalence of oscillation and nondisconjugacy
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- by G. B. Gustafson
- Proc. Amer. Math. Soc. 25 (1970), 254-260
- DOI: https://doi.org/10.1090/S0002-9939-1970-0284648-4
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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
- J. M. Dolan, Oscillatory behavior of solutions of linear ordinary differential equations of third order, Ph.D. Dissertation, University of Tennessee, Knoxville, Tenn., 1967.
—, On the relationship between the oscillatory behavior of a linear third-order equation and its adjoint, J. Differential Equations (to appear).
G. B. Gustafson, Conjugate point properties for $n$th order linear differential equations, Ph.D. Dissertation, Arizona State University, Tempe, Ariz., 1968.
- Maurice Hanan, Oscillation criteria for third-order linear differential equations, Pacific J. Math. 11 (1961), 919–944. MR 145160
- Philip Hartman, Ordinary differential equations, John Wiley & Sons, Inc., New York-London-Sydney, 1964. MR 0171038
Bibliographic Information
- © Copyright 1970 American Mathematical Society
- 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