Resolvent operators for integral equations in a Banach space

Grimmer, R. C.

doi:10.1090/S0002-9947-1982-0664046-4

Resolvent operators for integral equations in a Banach space
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Trans. Amer. Math. Soc. 273 (1982), 333-349 Request permission

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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