Uniqueness of Radial Solutions of Semilinear Elliptic Equations

E. Yanagida recently proved that the classical Matukuma equation with a given exponent has only one nite mass solution. We show how similar ideas can be exploited to obtain uniqueness results for other classes of equations as well as Matukuma equations with more general coeecients. One particular example covered is u + u p u = 0, with p > 1. The key ingredients of the method are energy functions and suitable transformations. We also study general boundary conditions, using an extension of a recent result by Bandle and Kwong. Yanagida's proof does not extend to solutions of Matukuma's equation satisfying other boundary conditions. We treat these with a completely diierent method of Kwong and Zhang.