New concentration phenomena for a class of radial fully nonlinear equations
Galise, Giulio1 ; Iacopetti, Alessandro2 ; Leoni, Fabiana1 ; Pacella, Filomena1
1 Dipartimento di Matematica, Sapienza Università di Roma, P.le Aldo Moro 2, 00185 Roma, Italy
2 Département de Mathématique, Université Libre de Bruxelles, Campus de la Plaine - CP214 boulevard du Triomphe, 1050, Bruxelles, Belgium
Annales de l'I.H.P. Analyse non linéaire, Tome 37 (2020) no. 5, pp. 1109-1141.
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We study radial sign-changing solutions of a class of fully nonlinear elliptic Dirichlet problems in a ball, driven by the extremal Pucci's operators and with a power nonlinear term. We first determine a new critical exponent related to the existence or nonexistence of such solutions. Then we analyze the asymptotic behavior of the radial nodal solutions as the exponents approach the critical values, showing that new concentration phenomena occur. Finally we define a suitable weighted energy for these solutions and compute its limit value.

DOI : 10.1016/j.anihpc.2020.03.003
Classification : 35J60, 35B50, 34B15
Mots-clés : Fully nonlinear Dirichlet problems, Radial solutions, Critical exponents, Sign-changing solutions, Asymptotic analysis
Galise, Giulio 1 ; Iacopetti, Alessandro 2 ; Leoni, Fabiana 1 ; Pacella, Filomena 1

1 Dipartimento di Matematica, Sapienza Università di Roma, P.le Aldo Moro 2, 00185 Roma, Italy
2 Département de Mathématique, Université Libre de Bruxelles, Campus de la Plaine - CP214 boulevard du Triomphe, 1050, Bruxelles, Belgium 
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     title = {New concentration phenomena for a class of radial fully nonlinear equations},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1109--1141},
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Galise, Giulio; Iacopetti, Alessandro; Leoni, Fabiana; Pacella, Filomena. New concentration phenomena for a class of radial fully nonlinear equations. Annales de l'I.H.P. Analyse non linéaire, Tome 37 (2020) no. 5, pp. 1109-1141. doi : 10.1016/j.anihpc.2020.03.003. http://archive.numdam.org/articles/10.1016/j.anihpc.2020.03.003/

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