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Proceedings of the American Mathematical Society

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Comparison theorem for conjugate points of systems of $n$th order nonselfadjoint differential equations


Author: E. C. Tomastik
Journal: Proc. Amer. Math. Soc. 96 (1986), 437-442
MSC: Primary 34C10; Secondary 47E05
DOI: https://doi.org/10.1090/S0002-9939-1986-0822435-8
MathSciNet review: 822435
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Abstract: A comparison theorem for conjugate points of the two systems of linear differential equations ${x^{(n)}} - {( - 1)^{n - k}}p(t)x = 0$ and ${y^{(n)}} - {( - 1)^{n - k}}q(t)y = 0$, where $p(t)$ and $q(t)$ are $m \times m$ matrices of continuous functions, is given. It is assumed that $q(t)$ is positive with respect to a certain cone but no positivity conditions of any kind are imposed on $p(t)$. No selfadjointness conditions are assumed; however, the results are new even in the selfadjoint case.


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Keywords: Conjugate point, comparison theorem, <IMG WIDTH="27" HEIGHT="37" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="${\mu _0}$">-positive operators with respect to a cone
Article copyright: © Copyright 1986 American Mathematical Society