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Recently, the horospherical $p$-Minkowski problem in hyperbolic space wasproposed as a counterpart of $L_p$ Minkowski problem in Euclidean space.Through designing a new volume preserving curvature flow, the existence ofnormalized even solution to the horospherical $p$-Minkowski problem was solvedfor all $p \in \mathbb{R}$. However, due to the lack of homogeneity of thehorospherical $p$-surface area measure, it is difficult to remove thenormalizing factor. In this paper, we overcome this difficulty for $-n\leq p<n$by the degree-theoretic approach.

Non-normalized solutions to the horospherical Minkowski problem