Resolvent operators for integral equations in a Banach space

Author:
R. C. Grimmer

Journal:
Trans. Amer. Math. Soc. **273** (1982), 333-349

MSC:
Primary 45N05; Secondary 34G10, 45D05

MathSciNet review:
664046

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Abstract: Conditions are given which ensure the existence of a resolvent operator for an integrodifferential equation in a Banach space. The resolvent operator is similar to an evolution operator for nonautonomous differential equations in a Banach space. As in the finite dimensional case, this operator is used to obtain a variation of parameters formula which can be used to obtain results concerning the asymptotic behaviour of solutions and weak solutions.

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DOI:
https://doi.org/10.1090/S0002-9947-1982-0664046-4

Article copyright:
© Copyright 1982
American Mathematical Society