Note on a family of Volterra equations

Author:
Kenneth B. Hannsgen

Journal:
Proc. Amer. Math. Soc. **46** (1974), 239-243

MSC:
Primary 45D05

DOI:
https://doi.org/10.1090/S0002-9939-1974-0350338-6

MathSciNet review:
0350338

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Abstract | References | Similar Articles | Additional Information

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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1974-0350338-6

Keywords:
Asymptotic behavior,
convex,
Hilbert space,
integro-differential equations,
selfadjoint linear operator,
viscoelasticity,
Volterra equations

Article copyright:
© Copyright 1974
American Mathematical Society