The authors discuss the bang-bang property for evolution inclusions in Banach spaces under a locally Lipschitz assumption on the multifunction, with respect to the state variable, and in the absence of any compactness conditions.
The problem looks hard since no results are available under weaker assumptions than globally Lipschitz-type conditions (in infinite dimension). The approach they adopt is Baire’s category method introduced by the authors in [Funkc. Ekvacioj, Ser. Int. 25, 153–162 (1982; Zbl 0535.34009)]. The deep results are presented in a plain style, understandable also to non expert readers. A rich reference list is also included.