Structure of radial solutions to Hénon type equation on the hyperbolic space

We consider Hénon type equation Δ H n u + ( sinh ⁡ r ) σ | u | p − 1 u = 0 in the hyperbolic space H n with n ≥ 2 , σ > 0 , p > 1 , and classify the positivity, stability and separation property of radial solutions which remained open in pioneering works by Hasegawa [9] , [10] , [11] . Main technical tool is a transformation ( Lemma 3.1 ), which enable us to work on the Euclidean space. As a byproduct, we reveal that Hasegawa's exponents p b and p c can be written explicitly by using the Sobolev type exponent p s and the Joseph–Lundgren type exponent p J L , respectively.