Note on a family of Volterra equations
Author:
Kenneth B. Hannsgen
Journal:
Proc. Amer. Math. Soc. 46 (1974), 239243
MSC:
Primary 45D05
MathSciNet review:
0350338
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Abstract: We prove that the solutions of a certain family of Volterra integrodifferential equations are uniformly bounded. We use this result to determine the asymptotic behavior of the solution of a Volterra equation in Hilbert space.
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 C. M. Dafermos, An abstract Volterra equation with applications to linear viscoelasticity, J. Differential Equations 7 (1970), 554569. MR 41 #4305. MR 0259670 (41:4305)
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 R. C. MacCamy and J. S. W. Wong, Stability theorems for some functional equations, Trans. Amer. Math. Soc. 164 (1972), 137. MR 45 #2432. MR 0293355 (45:2432)
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 D. F. Shea and S. Wainger, Variants of the WienerLévy theorem, with applications to stability problems for some Volterra integral equations, Amer. J. Math. (to appear). MR 0372521 (51:8728)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939197403503386
PII:
S 00029939(1974)03503386
Keywords:
Asymptotic behavior,
convex,
Hilbert space,
integrodifferential equations,
selfadjoint linear operator,
viscoelasticity,
Volterra equations
Article copyright:
© Copyright 1974
American Mathematical Society
