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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Stability criteria for Volterra equations
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by T. A. Burton and W. E. Mahfoud PDF
Trans. Amer. Math. Soc. 279 (1983), 143-174 Request permission

Abstract:

We consider a system of integro-differential equations of the form (1.1) \[ x’ = A(t)x + \int _0^t {C(t,s)x(s)\;ds} \] 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
  • © Copyright 1983 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 279 (1983), 143-174
  • MSC: Primary 45D05; Secondary 34D20, 45J05
  • DOI: https://doi.org/10.1090/S0002-9947-1983-0704607-8
  • MathSciNet review: 704607