On the radius continuity of the models of polytropic gas spheres which correspond to the positive solutions of the generalized Emden-Fowler equation

We completely answer the question which positive solutions of the Emden-Fowler equation , n > ½, m > ? 1, m+n > 0 induce models of polytropic gas spheres of finite radius or finite mass. We continue and complete the investigation of the radius continuity of these models initiated by van den Broek and Verhulst⁸ in connection with a numerical analysis by Hénon⁷.