Semilinear elliptic equations of the Henon type in hyperbolic space
This paper deals with a class of the semilinear elliptic equations of the Henon type in hyperbolic space. The problem involves a logarithm weight in the Poincare ball model, bringing singularities on the boundary. Considering radial functions, a compact Sobolev embedding result is proved, which extends a former Ni result made for a unit ball in RN. Combining this compactness embedding with the Mountain Pass Theorem, a result of the existence of positive solution is established.