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Zbl 0952.45005
Lizama, Carlos
Regularized solutions for abstract Volterra equations. (English)
[J] J. Math. Anal. Appl. 243, No.2, 278-292 (2000). ISSN 0022-247X

The author shows the existence, the uniqueness, and some qualitative properties of solutions for the abstract Volterra equation $$u(t) = f(t) + \int_{0}^{t}a(t-s)Au(s) ds,\quad t\in [0,T]$$ on a complex Banach space $X$ by means of an extended notion of resolvent, where $A$ is a closed linear unbounded operator with domain $D(A)$, $a \not=0$ is a scalar kernel, and $f \in C([0,T],X)$.
[Hu Chuangan (Tianjin)]

MSC 2000:: *45N05 Integral equations in abstract spaces
45D05 Volterra integral equations
47D03 (Semi)groups of linear operators

Keywords: abstract linear Volterra equations; convolution; $k$-regularized resolvents; semigroups of linear operators; Banach space

Cited in: Zbl 1106.45004

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