The well-posedness and the flow invariance are studied for a semilinear functional differential equation governed by a family of non-densely defined operators in a general Banach space. The notion of mild solutions is introduced through a new type of variation of constants formula and the well-posedness is established under a semilinear stability condition with respect to a metric-like functional and a subtangential condition. The abstract result is applied to a size-structured model with birth delay.
"Well-posedness and flow invariance for semilinear functional differential equations governed by non-densely defined operators." Differential Integral Equations 30 (9/10) 695 - 734, September/October 2017.