Rotationally Symmetric $p$-harmonic maps

TL;DR

This paper investigates rotationally symmetric p-harmonic maps through a second order ODE, establishing unique continuation, Liouville theorems, and analyzing the existence and asymptotic behavior of positive solutions.

Contribution

It provides new theoretical results on the existence, uniqueness, and asymptotic properties of positive solutions to the p-harmonic map equation in symmetric settings.

Findings

Unique continuation and Liouville theorems for positive solutions

Existence of bounded positive entire solutions

Asymptotic analysis of solutions

Abstract

We study a second order ordinary differential equation corresponding to rotationally symmetric $p$-harmonic maps. We show unique continuation and Liouville's type theorems for positive solutions. We discuss the existence of bounded positive entire solutions. Asymptotic properties of the positive solutions are investigated.