Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



On a functional equation arising in the stability theory of difference-differential equations

Authors: W. B. Castelan and E. F. Infante
Journal: Quart. Appl. Math. 35 (1977), 311-319
MSC: Primary 34K05
DOI: https://doi.org/10.1090/qam/492694
MathSciNet review: 492694
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Abstract: The functional differential equation

$\displaystyle Q'\left( t \right) = AQ\left( t \right) + B{Q^T}\left( {\tau - t} \right), - \infty < t < \infty $

, where $ A$, $ B$ are $ n \times n$ constant matrices, $ \tau \ge 0$, $ Q\left( t \right)$ is a differentiable $ n \times n$ matrix and $ {Q^T}\left( t \right)$ is its transpose, is studied. Existence, uniqueness and an algebraic representation of its solutions are given.

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DOI: https://doi.org/10.1090/qam/492694
Article copyright: © Copyright 1977 American Mathematical Society

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