✦ LIBER ✦

Regularized Solutions for Abstract Volterra Equations

✍ Scribed by Carlos Lizama

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 116 KB
Volume: 243
Category: Article
ISSN: 0022-247X
DOI: 10.1006/jmaa.1999.6668

No coin nor oath required. For personal study only.

✦ Synopsis

We introduce a two-kernel dependent family of strong continuous operators defined in a Banach space, which allows us to consider in an unified treatment the notions of, among others, C -semigroups of operators, cosine families, n-times 0 integrated semigroups, resolvent families and k-generalized solutions.

The results are applied to the study of existence and uniqueness of solutions for the Volterra equation of convolution type u s f q a) Au, in the case A is not necessarily densely defined. Examples for equations defined in L p spaces are also given.

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