On a class of nonlinear elliptic equations with fast increasing weight and critical growth

We are concerned with the existence of rapidly decaying solutions for the equation−div(K(x)∇u)=λK(x)|x|β|u|q−2u+K(x)|u|2∗−2u,x∈RN, where N⩾3, 2⩽q<2∗:=2N/(N−2), λ>0 is a parameter, K(x):=exp(|x|α/4), α⩾2 and the number β is given by β:=(α−2)(2∗−q)(2∗−2). We obtain a positive solution if 2