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Transactions of the American Mathematical Society

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Asymptotic solutions of linear Volterra integral equations with singular kernels


Authors: J. S. W. Wong and R. Wong
Journal: Trans. Amer. Math. Soc. 189 (1974), 185-200
MSC: Primary 45M05
DOI: https://doi.org/10.1090/S0002-9947-1974-0338718-0
MathSciNet review: 0338718
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Abstract: Volterra integral equations of the form $ u'(t) = - \smallint _0^ta(t - \tau )u(\tau )d\tau ,u(0) = 1$, are considered, where $ a(t) \in C(0,\infty ) \cap {L_1}(0,1)$. Explicit asymptotic forms are obtained for the solutions, when the kernels $ a(t)$ have a specific asymptotic representation.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1974-0338718-0
Keywords: Volterra integral equation, asymptotic form, Laplace transform, completely monotonic
Article copyright: © Copyright 1974 American Mathematical Society

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