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Proceedings of the American Mathematical Society

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

 
 

 

Oscillatory properties of linear third-order differential equations.


Author: W. J. Kim
Journal: Proc. Amer. Math. Soc. 26 (1970), 286-293
MSC: Primary 34.42
DOI: https://doi.org/10.1090/S0002-9939-1970-0264162-2
MathSciNet review: 0264162
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Abstract: Separation theorems, distribution of zeros of solutions, and disconjugacy criteria for linear third-order differential equations are discussed. For instance, it is proved that the equation $ y''' + py'' + qy' + ry = 0$, where $ p \in C'',q \in C'$, and $ r \in C$ on an interval $ I$, is disconjugate on $ I$ if $ p$ does not change sign and if $ q \leqq 0,r \geqq 0,q - 2p' \leqq 0$, and $ r - q' + p'' \leqq 0$ on $ I$.


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DOI: https://doi.org/10.1090/S0002-9939-1970-0264162-2
Keywords: Zeros of solutions, separation, distribution of zeros, sufficient conditions for disconjugacy, linear equations, ordinary, third-order, real-valued coefficients
Article copyright: © Copyright 1970 American Mathematical Society

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