Factorization and disconjugacy of third order differential equations

Zettl, Anton

doi:10.1090/S0002-9939-1972-0296421-3

Factorization and disconjugacy of third order differential equations
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by Anton Zettl

Proc. Amer. Math. Soc. 31 (1972), 203-208

DOI: https://doi.org/10.1090/S0002-9939-1972-0296421-3

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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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