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We study properties of !-limit sets of multivalued semiflows like chainrecurrence or the existence of cyclic chains. First, we prove that undercertain conditions the omega-limit set of a trajectory is chain recurrent,applying this result to an evolution differential inclusion with uppersemicontinous right-hand side. Second, we give conditions ensuring that theomega-limit set of a trajectory contains a cyclic chain. Using this result weare able to check that the omega-limit set of every trajectory of areaction-diffusion equation without uniqueness of solutions is an equilibrium.

Chain recurrence and structure of omega-limit sets of multivalued semiflows