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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A Volterra equation with square integrable solution


Author: Olof J. Staffans
Journal: Proc. Amer. Math. Soc. 78 (1980), 213-217
MSC: Primary 45D05; Secondary 45G10, 45J05
DOI: https://doi.org/10.1090/S0002-9939-1980-0550496-7
MathSciNet review: 550496
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Abstract: We study the asymptotic behavior of the solutions of the nonlinear Volterra integrodifferential equation

$\displaystyle x'(t) + \int_0^t {a(t - s)g(x(s))\;ds\; = f(t)\quad (t \in {R^ + }).} $

Here $ {R^ + } = [0,\infty ),a,g$ and f are given real functions, and x is the unknown solution. In particular, we give sufficient conditions which imply that x and x' are square integrable.

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DOI: https://doi.org/10.1090/S0002-9939-1980-0550496-7
Article copyright: © Copyright 1980 American Mathematical Society