A comparison between two theories for multi-valued semiflows and their asymptotic behaviour

This paper presents a comparison between two abstract frameworks in which one can treat multi-valued semiflows and their asymptotic behaviour. We compare the theory developed by Ball ( 1997) to treat equations whose solutions may not be unique, and that due to Melnik and Valero ( 1998) tailored more for differential inclusions. Although they deal with different problems, the main ideas seem quite similar. We study their relationship in detail and point out some essential technical problems in trying to apply Ball's theory to differential inclusions.