Semilinear elliptic equations of the Hénon-type in hyperbolic space (Q2796988)

The paper deals with a class of semilinear elliptic equations of Hénon type in hyperbolic spaces. The problem involves a logarithm weight in the Poincaré ball model, bringing singularities on the boundary. Considering radial functions, a compact Sobolev embedding result is proved, which extends a former result by \textit{W.-M. Ni} [Indiana Univ. Math. J. 31, 801--807 (1982; Zbl 0515.35033)] proved in the unit ball of \(\mathbb R^N\). Combining this compactness embedding with the Mountain Pass Theorem, the authors establish existence of positive solutions.