We study the local and global existence of mild solutions to a class of semilinear fractional Cauchy problems in the α-norm assuming that the operator in the linear part is the generator of a compact analytic C₀-semigroup. A suitable notion of mild solution for this class of problems is also introduced. The results obtained are a generalization and continuation of some recent results on this issue.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap103-2-4,
author = {Rong-Nian Wang and De-Han Chen and Yan Wang},
title = {The global existence of mild solutions for semilinear fractional Cauchy problems in the $\alpha$-norm},
journal = {Annales Polonici Mathematici},
volume = {105},
year = {2012},
pages = {161-173},
zbl = {1251.34095},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap103-2-4}
}
Rong-Nian Wang; De-Han Chen; Yan Wang. The global existence of mild solutions for semilinear fractional Cauchy problems in the α-norm. Annales Polonici Mathematici, Tome 105 (2012) pp. 161-173. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap103-2-4/