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Transactions of the American Mathematical Society

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



On nonlinear scalar Volterra integral equations. I

Author: Hans Engler
Journal: Trans. Amer. Math. Soc. 291 (1985), 319-336
MSC: Primary 45D05
MathSciNet review: 797063
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Abstract: The scalar nonlinear Volterra integral equation

$\displaystyle u(t) + \int_0^t {g(t,s,u(s))\,ds = f(t)\qquad (0 \leqslant t)} $

is studied. Conditions are given under which the difference of two solutions can be estimated by the variation of the difference of the corresponding right-hand sides. Criteria for the existence of $ \lim u(t)$ (as $ t \to \infty $) are given, and existence and uniqueness questions are also studied.

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Keywords: Nonlinear scalar Volterra equation, uniqueness, existence, continuous dependence on data, a priori estimates, asymptotic behavior, log-convex kernels
Article copyright: © Copyright 1985 American Mathematical Society

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