Singular limit and exact decay rate of a nonlinear elliptic equation

For any n≥3, 00, β>0, α≤β(n−2)/m, we prove the existence of radially symmetric solution of n−1mΔvm+αv+βx⋅∇v=0, v>0, in Rn, v(0)=η, without using the phase plane method. When 00 if 2β/(1−m)>max(α,0). For β>0 or α=0, we prove that the radially symmetric solution v(m) of the above elliptic equation converges uniformly on every compact subset of Rn to the solution of an elliptic equation as m→0.