2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64909We consider a fourth order partial differential equation in n-dimensional space introduced by Abreu in the context of Kähler metrics on toric orbifolds. Similarity solutions depending only on the radial coordinate in R^n are determined in terms of a second order ordinary differential equation. A local asymptotic analysis of solutions in the neighbourhood of singular points is carried out. The integrability (or otherwise) of Abreu's equation is discussed.Differential GeometrySymplectic Geometrytext