Olexiy V. Kapustyan (Taras Shevchenko National University of Kyiv), Pavlo O. Kasyanov (Institute for Applied System Analysis National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute) and José Valero (Universidad Miguel Hernández de Elche)

Abstract: We study properties of ω-limit sets of multivalued semiflows like chain recurrence or the existence of cyclic chains. First, we prove that under certain conditions the ω-limit set of a trajectory is chain recurrent, applying this result to an evolution differential inclusion with upper semicontinous right-hand side. Second, we give conditions ensuring that the ω-limit set of a trajectory contains a cyclic chain. Using this result we are able to check that the ω-limit set of every trajectory of a reaction-diffusion equation without uniqueness of solutions is an equilibrium.