Uniqueness of positive solutions to the rotationally symmetric p-harmonic map equations

Let α and β be positive solutions on (0, ∞) to the rotationally symmetric p-harmonic map equation on model manifolds M(f) and M(g), where f is assumed to be sufficiently large near infinity and g″(y) ⩾ 0 for y > 0. We show that if α and β have the same limit at infinity, then α ≡ β on (0, ∞).