Multiple closed geodesics on Riemannian 3-spheres

In this paper, we prove that for every Riemannian Q-homological 3-sphere (M, g) with injectivity radius \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$inj(M)\ge \pi$$\end{document} and the sectional curvature K satisfying \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\frac{1}{16} < K \le 1}$$\end{document} there exist at least two geometrically distinct closed geodesics.