Rotationally Symmetric F-harmonic Maps Equations

TL;DR

This paper investigates rotationally symmetric F-harmonic maps between noncompact manifolds, establishing unique continuation, Liouville theorems, and analyzing the asymptotic behavior and existence of bounded solutions.

Contribution

It provides new results on the uniqueness, asymptotics, and existence of solutions for F-harmonic maps under symmetry assumptions.

Findings

Unique continuation and Liouville theorems proved for positive solutions.

Asymptotic properties of solutions characterized.

Existence of bounded positive solutions established.

Abstract

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