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Proceedings of the American Mathematical Society

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

 

 

Factorization and disconjugacy of third order differential equations


Author: Anton Zettl
Journal: Proc. Amer. Math. Soc. 31 (1972), 203-208
MSC: Primary 34C10
MathSciNet review: 0296421
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Abstract: Sufficient conditions for the factorization of $ y''' + py'' + qy' + ry$ into a product of first order operators as well as into a product of a first order and a second order operator are given. Factorization into a product of first order factors is known to be equivalent to disconjugacy. These conditions are simple inequalities involving the coefficients.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0296421-3
Keywords: Ordinary differential equations, disconjugacy criteria, factorization of differential operators, Frobenius factorization, Pólya's property ``W", Wronskians, oscillation or nonoscillation of solutions, zeros of solutions, third order linear homogeneous differential equations, Tchebycheff property of solutions
Article copyright: © Copyright 1972 American Mathematical Society