Eventual disconjugacy of selfadjoint fourth order linear differential equations

Author:
G. B. Gustafson

Journal:
Proc. Amer. Math. Soc. **35** (1972), 187-192

MSC:
Primary 34C10

DOI:
https://doi.org/10.1090/S0002-9939-1972-0298126-1

MathSciNet review:
0298126

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Abstract | References | Similar Articles | Additional Information

Abstract: At the 1969 Differential Equations Conference held at Knoxville, Tennessee, Z. Nehari asked the following question about fourth-order selfadjoint linear differential equations: ``Assume that solutions of the equation have only a finite number of zeros on . Does there exist a half-line on which no solution of the equation has more than three zeros?'' In this paper sufficient conditions are given for the equation to have the property that solutions possess only a finite number of zeros. This theorem is then used to construct an example which answers the above question in the negative. The example also shows that if on each half-line the equation has a solution with two consecutive double zeros, then it need not follow that there is a solution with infinitely many zeros.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1972-0298126-1

Keywords:
Oscillation,
nonoscillation,
disconjugacy,
eventually disconjugate,
disconjugate in the sense of Reid,
*p*th conjugate point

Article copyright:
© Copyright 1972
American Mathematical Society