Positive solutions for nonlinear elliptic equations with fast increasing weights

We find positive rapidly decaying solutions for the equation − div(K(x)∇u) = K(x)u2∗−1 + λK(x)|x|α−2u in RN, where N 3, the nonlinearity is given by the critical Sobolev exponent 2 ∗ = 2N/(N − 2), the weight is K(x) = exp ( 14 |x|α), α 2 and λ is a parameter. 1