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Comparison theorems for eigenvalue problems for $ n$th order differential equations


Authors: Darrel Hankerson and Allan Peterson
Journal: Proc. Amer. Math. Soc. 104 (1988), 1204-1211
MSC: Primary 34B25; Secondary 34C10, 47B55
DOI: https://doi.org/10.1090/S0002-9939-1988-0946624-9
MathSciNet review: 946624
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Abstract: We give a comparison theorem for eigenvalues for a $ (k,n - k)$-conjugate boundary value problem for the systems $ {( - 1)^{n - k}}Ly = \lambda P(t)y$ and $ {( - 1)^{n - k}}Lz = \Lambda Q(t)z$, where $ P(t)$ and $ Q(t)$ are continuous $ m \times m$ matrix functions. We assume that the corresponding scalar equation $ Lx = 0$ is $ (j,n - j)$-disconjugate for $ k - 1 \leq j \leq n - 1$. A special case of this is when $ Lx = 0$ is disconjugate; our results are new even in this case.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0946624-9
Keywords: Comparison theorem, boundary value problem, $ {u_0}$-positive operator, disconjugacy
Article copyright: © Copyright 1988 American Mathematical Society

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