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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

An $ L\sp{1}$ remainder theorem for an integrodifferential equation with asymptotically periodic solution


Author: Kenneth B. Hannsgen
Journal: Proc. Amer. Math. Soc. 73 (1979), 331-337
MSC: Primary 45D05; Secondary 45J05, 45M05
MathSciNet review: 518514
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Abstract: For a certain integrodifferential equation of Volterra type on $ (0,\infty )$, with piecewise linear convolution kernel, it is shown that the solution is $ u(t) = \alpha \;\cos \beta t + \rho (t)$, with $ \rho \in {L^1}(0,\infty )$ and $ \alpha $ and $ \beta $ constant; $ u'$ is represented similarly.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1979-0518514-1
PII: S 0002-9939(1979)0518514-1
Article copyright: © Copyright 1979 American Mathematical Society