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Resolvent Operators for Integral Equations in a Banach Space

1982
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Transactions of the American Mathematical Society
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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. 1. Introduction. In this paper we shall be

doi:10.2307/1999209
fatcat:y7r3hjdm6zcthnb5vizqul34we