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Selfadjoint nonoscillatory second order linear $ B\sp \ast$-algebra differential equations


Author: Manuel Lopez
Journal: Proc. Amer. Math. Soc. 97 (1986), 71-74
MSC: Primary 34G10; Secondary 34C10, 46K99
DOI: https://doi.org/10.1090/S0002-9939-1986-0831390-6
MathSciNet review: 831390
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Abstract: The main result in this paper states that the second order linear $ {B^*}$-algebra differential equation $ (p(t)y') + q(t)y = 0$, where $ p(t)$ is positive and $ q(t)$ is Hermitian for each $ t$, is nonoscillatory on $ [{t_0},\infty )$ if the scalar equation $ ({\left\Vert {{p^{ - 1}}(t)} \right\Vert^{ - 1}}W')' + \left\Vert {q(t)} \right\Vert W = 0$ is nonoscillatory on $ [{t_0},\infty )$.

Consequently, every criterion on nonoscillation in the scalar case automatically produces another one in the $ {B^*}$-algebra case.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1986-0831390-6
Article copyright: © Copyright 1986 American Mathematical Society

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