A very singular solution for the slow diffusion equation with nonlinear convection

We here investigate an existence and uniqueness of the nontrivial, nonnegative solution of a nonlinear ordinary differential equation:(fm)″+βrf′+αf+σ(fq)′=0(fm)″+βrf′+αf+σ(fq)′=0 satisfying a specific decay rate: limr→∞rα/βf(r)=0limr→∞rα/βf(r)=0 with α=1/(2q−m−1)α=1/(2q−m−1) and β=(q−m)/(2q−m−1)β=(q−m)/(2q−m−1). Here m>1m>1, m