A Neumann problem with logarithmic nonlinearity in a ball

The nonlinear elliptic problem −Δu=logu+h(x)up−Δu=logu+h(x)up in a ball BR⊂RnBR⊂Rn with Neumann boundary conditions ∂νu=0∂νu=0 on ∂BR∂BR were studied. By means of a double perturbation argument, we obtain a positive radial solution u∈C2(B¯R∖{0})∩C(B¯R).