Preprint

Inserted: 26 may 2026

Pages: 24
Year: 2026

Abstract:

In this article, we study higher-order Bol's inequality for radial normal solutions to a singular Liouville equation. By applying these inequalities along with compactness arguments, we derive necessary and sufficient conditions for the existence of radial normal solutions to a singular Q-curvature problem. Moreover, under suitable assumptions on the Q-curvature, we obtain uniform bounds on the total Q-curvature.

Keywords: Q-curvature, Liouville equation, Pohozaev identity, Bol’s inequality, Normal solution