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Existence for a class of partial differential equations with nonlocal conditions

✍ Scribed by Hsiang Liu; Jung-Chan Chang

Publisher: Elsevier Science
Year: 2009
Tongue: English
Weight: 552 KB
Volume: 70
Category: Article
ISSN: 0362-546X
DOI: 10.1016/j.na.2008.04.009

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✦ Synopsis

This paper is concerned with the existence of mild and classical solutions of nonlocal Cauchy problems. We assume that the linear part generates an analytic compact bounded semigroup, and that the nonlinear part is a Hölder continuous function with respect to the fractional power norm of the linear part. Considering the nonlocal conditions in the α-norm, we generalize the recent conclusions on this topic. The results obtained will be applied to a class of functional partial differential equations with nonlocal conditions in 1 2 -norm.

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