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" In this paper, we study the following semi-linear elliptic equation -0394_H^nu=|u|^p-2u, qquad qquad (0.1) in the whole Hyperbolic space mathbbH^n,where n 2265 3, p 203a 2n\/(n-2). We obtain some regularity results for the radial singular solutions of problem (0.1). We show that the singular solution u^2217 with lim_t 2192 0(sinht)^ frac2p-2 22c5u(t)=00b1( frac2p-2(n-2- frac2p-2)^ frac1p-2 belongs to the closure (in the natural topology given by H00b9_loc( mathbbH^N)2229L^p_loc(H^N)) of the set of smooth classical solutions to the Eq. (0.1). In contrast, we also prove that any oscillating radial solutions of (0.1) on mathbbH^N\{0 fails to be in the space H00b9_loc( mathbbH^N)2229L^p_loc(H^N).", number=2, journal=Journal of Partial Differential Equations, year=2015, month=June, pages=120–127