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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Stability criteria for Volterra equations


Authors: T. A. Burton and W. E. Mahfoud
Journal: Trans. Amer. Math. Soc. 279 (1983), 143-174
MSC: Primary 45D05; Secondary 34D20, 45J05
MathSciNet review: 704607
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Abstract: We consider a system of integro-differential equations of the form (1.1)

$\displaystyle x^{\prime} = A(t)x + \int_0^t {C(t,s)x(s)\;ds} $

with $ A$ and $ C$ being $ n \times n$ matrices. Various types of stability are defined and results are obtained showing when one type of stability is equivalent to another type. We also construct a number of Lyapunov functional from which we obtain necessary and sufficient conditions for stability of (1.1). Finally, we prove several results concerning qualitative behavior of solutions of (1.1).

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1983-0704607-8
PII: S 0002-9947(1983)0704607-8
Article copyright: © Copyright 1983 American Mathematical Society