In this paper, we prove that on every Finsler $n$-sphere $(S^n, F)$ with reversibility $\lambda$ satisfying $F^2<(\frac{ \lambda+1}{ \lambda})^2g_0$ and $l(S^n, F)\ge \pi(1+\frac{ 1}{ \lambda})$, there always exist at least $n$ prime closed geodesics without self-intersections, where $g_0$ is the standard Riemannian metric on $S^n$ with constant curvature 1 and $l(S^n, F)$ is the length of a shortest geodesic loop on $(S^n, F)$. We also study the stability of these closed geodesics.
Categories: math.DG