Elliptic closed geodesics on non-negatively curved Finsler manifolds

In this paper, we prove that if a compact simply-connected manifold $(M,F)$ with a bumpy irreversible Finsler metric $F$ whose flag curvature $K$ satisfies $K\ge 0$ and $H^{\ast }(M;\text{Q})\cong T_{d,n+1}(x)$ for some $d\in 2\mathbb{N}$ and $n\in \mathbb{N}$ carries exactly $\frac{dn(n+1)}{2}$ (the number of closed geodesics in Katok’s example) closed geodesics, then there are at least $2$ irrationally elliptic closed geodesics on $(M,F)$.