Uniqueness of Mass-Conserving Self-similar Solutions to Smoluchowski's Coagulation Equation with Inverse Power Law Kernels

Uniqueness of mass-conserving self-similar solutions to Smoluchowski's coagulation equation is shown when the coagulation kernel K is given by $K(x,x_{\ast })=2(x{x}_{\ast }{)}^{-\alpha }$, $(x,x_{\ast })\in (0,\infty {)}^2$, for some $\alpha >0$.