Existence of closed geodesics on Finsler nn-spheres

In this paper, we prove that on every Finsler nn-sphere (Sn,F)(Sn,F) with reversibilityλλ satisfying F2<(λ+1λ)2g0 and l(Sn,F)≥π(1+1λ), there always exist at least nn prime closed geodesics without self-intersections, where g0g0 is the standard Riemannian metric on SnSn with constant curvature 11 and l(Sn,F)l(Sn,F) is the length of a shortest geodesic loop on (Sn,F)(Sn,F). We also study the stability of these closed geodesics.