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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
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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DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0822435-8
PII: S 0002-9939(1986)0822435-8
Keywords: Conjugate point, comparison theorem, $ {\mu _0}$-positive operators with respect to a cone
Article copyright: © Copyright 1986 American Mathematical Society