Abstract
Existence of stationary solutions to the coagulation-fragmentation equation is shown when the coagulation kernel K and the overall fragmentation rate a are given by K(x,y)=xαyβ+xβyα and a(x)=xγ, respectively, with 0≤α≤β≤1, α+β∈[0,1), and γ>0. The proof requires two steps: a dynamical approach is first used to construct stationary solutions under the additional assumption that the coagulation kernel and the overall fragmentation rate are bounded from below by a positive constant. The general case is then handled by a compactness argument.
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