A UNIFIED APPROACH TO MATUKUMA TYPE EQUATIONS ON THE HYPERBOLIC SPACE OR ON A SPHERE

摘要

In this note, we consider the following Matukuma type equation on the hyperbolic space or on a spherical cap of the unit sphere under the homogeneous Dirichlet boundary condition Λu + K(x)u_+~p = 0, where Λ is the Laplace-Beltrami operator on the hyperbolic space or on the unit sphere. Under suitable assumptions on K, we determine the structure of positive solutions.