New concentration phenomena for a class of radial fully nonlinear equations

被引：2
作者：
Galise, Giulio [1 ]
Iacopetti, Alessandro [2 ]
Leoni, Fabiana [1 ]
Pacella, Filomena [1 ]
机构：
[1] Sapienza Univ Roma, Dipartimento Matemat, Ple Aldo Moro 2, I-00185 Rome, Italy
[2] Univ Libre Bruxelles, Dept Math, Campus Plaine,CP214 Blvd Triomphe, B-1050 Brussels, Belgium
来源：
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2020年 / 37卷 / 05期
关键词：
Fully nonlinear Dirichlet problems; Radial solutions; Critical exponents; Sign-changing solutions; Asymptotic analysis; SIGN-CHANGING SOLUTIONS; BREZIS-NIRENBERG PROBLEM; ASYMPTOTIC ANALYSIS;
D O I：
10.1016/j.anihpc.2020.03.003
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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. (C) 2020 Elsevier Masson SAS. All rights reserved.
引用
收藏
页码：1109 / 1141
页数：33
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