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An abstract linear Volterra equation with a nonconvolution kernel


Author: T. Kiffe
Journal: Proc. Amer. Math. Soc. 82 (1981), 51-57
MSC: Primary 45N05; Secondary 45D05
DOI: https://doi.org/10.1090/S0002-9939-1981-0603600-7
MathSciNet review: 603600
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Abstract: This paper is concerned with the existence and uniqueness of solutions to the equation $ x(t) + \int_0^t {a(t,\tau )Ax(\tau )d\tau = f(t)} $ where $ A$ is an unbounded, positive, selfadjoint operator on a Hilbert space. A representation is given for the solution of this equation.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0603600-7
Article copyright: © Copyright 1981 American Mathematical Society

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