Sublinear elliptic problems under radiality. Harmonic NA groups and Euclidean spaces

2017/11/06 by Damek, Ewa, Ghardallou, Zeineb
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1711.01931

Abstract

Let Ł be the Laplace operator on \R ^d, d≥ 3 or the Laplace Beltrami operator on the harmonic NA group (in particular on a rank one noncompact symmetric space). For the equation Łu - φ(⋅,u)=0 we give necessary and sufficient conditions for the existence of entire bounded or large solutions under the hypothesis of radiality of φ with respect to the first variable. A Harnack-type inequality for positive continuous solutions is also proved.

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