In this paper, we continue to construct stationary classical solutions for the incompressible planar flows approximating singular stationary solutions of this problem. This procedure is carried out by constructing solutions for the following elliptic equations

where 0 <

*p* < 1, Ω ? R

^{2} is a bounded simply-connected smooth domain,

*κ*_{i} (i=1, …,

*k*) is prescribed positive constant. The result we prove is that for any given non-degenerate critical point

**x**_{0}=(

*x*_{0,1}, …,

*x*_{0,k}) of the Kirchhoff-Routh function defined on Ω

^{k} corresponding to (

*κ*_{1}, …,

*κ*_{k}), there exists a stationary classical solution approximating stationary

*k* points vortex solution. Moreover, as λ → +∞, the vorticity set {

*y*:

*u*_{λ} >

*κ*_{j}} ∩

*B*_{δ}(

*x*_{0,j}) shrinks to {

*x*_{0,j}}, and the local vorticity strength near each

*x*_{0,j} approaches

*κ*_{j},

*j*=1, …,

*k*. This result makes the study of the above problem with

*p* ≥ 0 complete since the cases

*p* > 1,

*p*=1,

*p*=0 have already been studied in [11, 12] and [13] respectively.