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A unified approach to Matukuma type equations on the hyperbolic space or on a sphere

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  • 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 \begin{eqnarray*} \Lambda u+K(x)u_+^{p}=0, \end{eqnarray*} where $\Lambda$ 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.
    Mathematics Subject Classification: Primary: 35J15; Secondary: 35J61, 58J05.

    Citation:

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