Closed geodesics on Finsler spheres

In this paper, we prove that for every Finsler n-sphere (S ⁿ ,?F) all of whose prime closed geodesics are non-degenerate with reversibility λ and flag curvature K satisfying ${\left(\frac{\lambda}{\lambda+1}\right)^2 < K \le 1,}$ there exist ${2\frac{n+1}{2}]-1}$ prime closed geodesics; moreover, there exist ${2\frac{n}{2}]-1}$ non-hyperbolic prime closed geodesics provided the number of prime closed geodesics is finite.