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Disconjugacy and oscillation of third order differential equations with nonnegative coefficients


Authors: G. J. Etgen and C. D. Shih
Journal: Proc. Amer. Math. Soc. 38 (1973), 577-582
MSC: Primary 34C10
DOI: https://doi.org/10.1090/S0002-9939-1973-0320432-3
MathSciNet review: 0320432
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Abstract: The purpose of this paper is to establish conditions which imply that the third order linear differential equation with nonnegative coefficients defined on an infinite interval will fail to be disconjugate on any infinite subinterval. Assuming that the equation is not disconjugate on any infinite subinterval, conditions are presented which establish that the equation has oscillatory solutions. These results are in partial answer to questions raised by J. H. Barrett. The oscillation criteria obtained here are similar to the oscillation conditions established by A. C. Lazer.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0320432-3
Keywords: Third order linear differential equations, disconjugacy, oscillation of solutions
Article copyright: © Copyright 1973 American Mathematical Society