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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Stability of solutions of linear systems with dominant main diagonal

Author: Charles Kahane
Journal: Proc. Amer. Math. Soc. 33 (1972), 69-71
MSC: Primary 34D99
MathSciNet review: 0294799
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Abstract: We establish the asymptotic stability of solutions of a first order linear system of differential equations in which the matrix characterizing the system has a dominating principal diagonal with negative entries; the domination is expressed through the condition that, numerically, each entry in the principal diagonal exceeds the sum of the absolute values of the remaining entries in the same column.

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Keywords: Stability, linear differential system, matrices with dominant main diagonal
Article copyright: © Copyright 1972 American Mathematical Society