BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Filomena Pacella (U. Roma\, Sapienza) DTSTART:20200528T130000Z DTEND:20200528T140000Z DTSTAMP:20260423T024806Z UID:RJWAPDE/7 DESCRIPTION:Title: Critical exponents for a class of fully nonlinear equations\nby Filome na Pacella (U. Roma\, Sapienza) as part of Rio de Janeiro webinar on analy sis and partial differential equations\n\n\nAbstract\nWe consider a class of radial fully nonlinear equations involving the extremal Pucci's operato rs and power nonlinearities.\nFor such equations some critical exponents w ere introduced by P.Felmer and A.Quaas in 2003\, motivated by the study of positive entire radial solutions.\nIn the first part of the talk I will d iscuss the role and properties of such exponents and its relation with con centration phenomena and energy invariance.\nIn the second part I will pre sent an alternative proof of the existence and uniqueness of these critica l exponents\, entirely based on the study of an associated quadratic dynam ical system. This approach also allows to get in a unified and simple way new existence and classification results for singular solutions as well as to prove that the same critical exponents give a threshold for the existe nce or nonexistence of positive radial solutions for the Dirichlet problem in exterior domains. This last result was recently proved by G.Galise\, A.Iacopetti and F. Leoni (2019) with a different proof.\nThe results prese nted are contained in several joint papers with I.Birindelli\, G.Galise\, F.Leoni\, L.Maia\, G.Saller Nornberg.\n\nTo join Prof. Pacella's talk\, pl ease use the following information.\n\nLink to join the talk:\nhttps://puc -rio.zoom.us/j/91799849377?pwd=bjU4MkpMdC9sWit3bGJQNTBQcnY3UT09\n\nMeeting ID: 917 9984 9377\nPassword: 801822\n LOCATION:https://researchseminars.org/talk/RJWAPDE/7/ END:VEVENT END:VCALENDAR