New concentration phenomena for a class of radial fully nonlinear\n equations

2019/12/02 by Giulio Galise, Alessandro Iacopetti, Galise, Giulio +5
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1912.00847

openalex publication_date 2019/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study radial sign-changing solutions of a class of fully nonlinear\nelliptic Dirichlet problems in a ball, driven by the extremal Pucci's operators\nand with a power nonlinear term. We first determine a new critical exponent\nrelated to the existence or nonexistence of such solutions. Then we analyze the\nasymptotic behavior of the radial nodal solutions as the exponents approach the\ncritical values, showing that new concentration phenomena occur. Finally we\ndefine a suitable weighted energy for these solutions and compute its limit\nvalue.\n

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