We establish existence of mild solutions for the semilinear first order functional abstract Cauchy problem and we prove that the set of mild solutions of this problem is connected in the space of continuous functions.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap81-2-7, author = {Hern\'an R. Henr\'\i quez and Genaro Castillo G.}, title = {The Kneser property for the abstract Cauchy problem}, journal = {Annales Polonici Mathematici}, volume = {81}, year = {2003}, pages = {167-181}, zbl = {1042.47038}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap81-2-7} }
Hernán R. Henríquez; Genaro Castillo G. The Kneser property for the abstract Cauchy problem. Annales Polonici Mathematici, Tome 81 (2003) pp. 167-181. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap81-2-7/