Radial singular solutions for the N-Laplace Equation with exponential nonlinearities

2018/07/16 by Marius Ghergu, Jacques Giacomoni, Ghergu, M. +3 · 2 citations
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.1807.05918

openalex publication_date 2018/07/16 · openalex created_date 2018/08/03 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider radial distributional solutions of the quasilinear equation -Δ_N u=f(u) in the punctured open ball B_R\backslash\0\⊂ \RR^N, N ≥ 2. We obtain sharp conditions on the nonlinearity f for extending such solutions to the whole domain B_R by preserving the regularity. For a certain class of noninearity f we obtain the existence of singular solutions and deduce upper and lower estimates on the growth rate near the singularity.

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• Infinite concentration and oscillation estimates for supercritical semilinear elliptic equations in discs. II
• Infinite concentration and oscillation estimates for supercritical semilinear elliptic equations in discs. I

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