Uniqueness of radial solutions of semilinear elliptic equations on hyperbolic space

We consider the uniqueness of radial solutions for the semilinear elliptic equation −ΔHdu+λu−up+1=0−ΔHdu+λu−up+1=0 on hyperbolic space HdHd. The proof is based on suitable transformations, energy functions and an idea of Yanagida. A similar approach was used by Kwong and Li.