MR2297943 Liu, James, N'Guérékata, Gaston, Minh, Nguyen Van and Vu, Quoc Phong James LIU, Gaston N'GUÉRÉKATA, Nguyen Van MINH and Quoc Phong VU Bounded Solutions of Parabolic Equations in Continuous Function Spaces Funkcialaj Ekvacioj. Serio Internacia 49 2006 337--355 http://fe.math.kobe-u.ac.jp/FE/FullPapers/49-3/49_337.pdf http://www.ams.org/mathscinet-getitem?mr=MR2297943 This paper is concerned with the existence of bounded mild solutions to equations of the form $u'(t)=Au(t)+f(t)$, where $A$ generates a holomorphic semigroup that is not necessarily strongly continuous, and $f$ is a bounded function. This problem arises when one considers a parabolic equation in spaces of continuous functions. The obtained results, that are stated in terms of spectral properties of the spectrum of $A$ and the uniform spectrum of $f$, extend previous ones. Parabolic equation, Continuous function space, Complete second order evolution equation, Mild solution. 34G10, 35K90. 49-337 2006 Bounded Solutions of Parabolic Equations in Continuous Function Spaces LIU, James, N'GUÉRÉKATA, Gaston, MINH, Nguyen Van and VU, Quoc Phong James LIU, Gaston N'GUÉRÉKATA, Nguyen Van MINH and VU Quoc Phong
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