{"id":16841,"date":"2020-06-18T07:54:17","date_gmt":"2020-06-18T07:54:17","guid":{"rendered":"http:\/\/cio.edu.umh.es\/?p=16841"},"modified":"2021-07-22T09:50:07","modified_gmt":"2021-07-22T07:50:07","slug":"chain-recurrence-and-structure-of-%cf%89-limit-sets-of-multivalued-semiflows-2020-communications-on-pure-and-applied-analysis-19-4-pp-2197-2217","status":"publish","type":"post","link":"https:\/\/cio.umh.es\/en\/2020\/06\/18\/chain-recurrence-and-structure-of-%cf%89-limit-sets-of-multivalued-semiflows-2020-communications-on-pure-and-applied-analysis-19-4-pp-2197-2217\/","title":{"rendered":"Chain recurrence and structure of \u03c9-limit sets of multivalued semiflows (2020), Communications on pure and applied analysis 19 (4), pp. 2197\u20132217"},"content":{"rendered":"<p><strong>Olexiy V. Kapustyan<\/strong> (<em>Taras Shevchenko National University of Kyiv<\/em>),<strong> Pavlo O. Kasyanov<\/strong> (I<em>nstitute for Applied System Analysis National Technical University of Ukraine \u201cIgor Sikorsky Kyiv Polytechnic Institute<\/em>) and <strong>Jos\u00e9 Valero\u00a0<\/strong>(<em>MHU<\/em>)<\/p>\n<p><strong>Abstract:<\/strong> We study properties of \u03c9-limit sets of multivalued semiflows like chain recurrence or the existence of cyclic chains. First, we prove that under certain conditions the \u03c9-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 \u03c9-limit set of a trajectory contains a cyclic chain. Using this result we are able to check that the \u03c9-limit set of every trajectory of a reaction-diffusion equation without uniqueness of solutions is an equilibrium.<\/p>","protected":false},"excerpt":{"rendered":"<p>Olexiy V. Kapustyan (Taras Shevchenko National University of Kyiv), Pavlo O. Kasyanov (Institute for Applied System Analysis National Technical University of Ukraine \u201cIgor Sikorsky Kyiv Polytechnic Institute) and Jos\u00e9 Valero\u00a0(Universidad Miguel Hern\u00e1ndez de Elche)<br \/>\nAbstract: We study properties of \u03c9-limit sets of multivalued semiflows like chain recurrence or the existence of cyclic chains. First, we prove [&#8230;]<\/p>","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_links_to":"","_links_to_target":""},"categories":[369888],"tags":[],"_links":{"self":[{"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/posts\/16841"}],"collection":[{"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/comments?post=16841"}],"version-history":[{"count":0,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/posts\/16841\/revisions"}],"wp:attachment":[{"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/media?parent=16841"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/categories?post=16841"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/tags?post=16841"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}