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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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: http://dx.doi.org/10.1090/S0002-9947-1982-0664046-4
PII: S 0002-9947(1982)0664046-4
Article copyright: © Copyright 1982 American Mathematical Society