This paper deals with the existence of solutions to the elliptic equation −u−
µ u
|x|2 = u + |u|2∗−2u + f(x, u) in
, u = 0 on @
, where
is a bounded domain in
RN(N ≥ 3), 0 ∈
, 2 = 2N
N−2 , > 0, 6∈ µ, µ is the spectrum of the operator
− − µI
|x|2 with zero Dirichlet boundary condition, 0 < µ < ¯µ, ¯µ = (N−2)2
4 , f(x, u) is
an asymmetric lower order perturbation of |u|2∗−1 at infinity. Using the dual variational
methods, the existence of nontrivial solutions is proved.
