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Asymptotic behavior of solutions of Volterra integro-differential equations


Authors: M. Rama Mohana Rao and P. Srinivas
Journal: Proc. Amer. Math. Soc. 94 (1985), 55-60
MSC: Primary 45J05
DOI: https://doi.org/10.1090/S0002-9939-1985-0781056-5
MathSciNet review: 781056
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Abstract: The asymptotic behavior of solutions of Volterra integrodifferential equations of the form

$\displaystyle x'(t) = A(t)x(t) + \int_0^t {K(t,s)} x(s)ds + F(t)$

is discussed in which $ A$ is not necessarily a stable matrix. An equivalent equation which involves an arbitrary function is derived and a proper choice of this function would pave a way for the new coefficient matrix $ B$ (corresponding $ A$) to be stable.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1985-0781056-5
Keywords: Integro-differential equation, equivalent equation, arbitrary function, differential resolvent
Article copyright: © Copyright 1985 American Mathematical Society

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