Let be the - not necessarily densely defined - generator of an analytic semigroup acting in some Banach space . In the paper we prove a general theorem about the existence and uniqueness of solutions of
Our main assumption with respect to the non-linearity is that is locally Lipschitz continuous with respect to certain intermediate spaces between and . Our theorem extends results obtained by W. von Wahl  and A. Lunardi . In the second part this theorem is applied to the Cahn-Hilliard equation with Dirichlet boundary conditions.
Cite this article
M. Uiterdijk, On a Theorem by W. von Wahl. Z. Anal. Anwend. 16 (1997), no. 4, pp. 961–978DOI 10.4171/ZAA/799