Critical exponents for a class of fully nonlinear equations

Abstract: We consider a class of radial fully nonlinear equations involving the extremal Pucci's operators and power nonlinearities. For such equations some critical exponents were introduced by P.Felmer and A.Quaas in 2003, motivated by the study of positive entire radial solutions. In the first part of the talk I will discuss the role and properties of such exponents and its relation with concentration phenomena and energy invariance. In the second part I will present an alternative proof of the existence and uniqueness of these critical exponents, entirely based on the study of an associated quadratic dynamical 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 existence 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. The results presented are contained in several joint papers with I.Birindelli, G.Galise, F.Leoni, L.Maia, G.Saller Nornberg.

analysis of PDEs

Audience: researchers in the topic

Comments: To join Prof. Pacella's talk, please use the following information.

Link to join the talk: puc-rio.zoom.us/j/91799849377?pwd=bjU4MkpMdC9sWit3bGJQNTBQcnY3UT09

Meeting ID: 917 9984 9377 Password: 801822

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Rio de Janeiro webinar on analysis and partial differential equations

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