  We extend two celebrated theorems on closed geodesics of Riemannian 2-spheres
to the larger class of reversible Finsler 2-spheres: Lusternik-Schnirelmann's
theorem asserting the existence of three simple closed geodesics, and
Bangert-Franks-Hingston's theorem asserting the existence of infinitely many
closed geodesics. In order to prove the first theorem, we employ the
generalization of Grayson's curve shortening flow developed by Angenent-Oaks.
