2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/131976We prove that for every $\Q$-homological Finsler 3-sphere $(M,F)$ with a bumpy and irreversible metric $F$, either there exist two non-hyperbolic prime closed geodesics, or there exist at least three prime closed geodesics.17 pages. Some modifications have been made. accepted by Calc. Var. & PDEsDifferential Geometrytext