We devote the present paper to studying a critical exponent with respect to the stability of solutions to Hénon type equation on the hyperbolic space. In order to specify the critical exponent, we prove the existence and nonexistence result for stable solutions. In this paper, we obtain stable, positive, and radial solutions of the Hénon type equation for the supercritical case. Moreover, we prove that the set of these stable solutions has the separation structure.
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