Uniqueness of mass-conserving self-similar solutions to Smoluchowski's coagulation equation with inverse power law kernels

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