Infinitely many nonradial solutions for the Hénon equation with critical growth

We consider the following Hénon equation with critical growth: (∗) { −Δu = |y|α uN+2 N−2 , u > 0 y ∈ B1(0), u = 0, on ∂B1(0), where α > 0 is a positive constant, B1(0) is the unit ball in R N , and N ≥ 4. Ni [9] proved the existence of a radial solution and Serra [12] proved the existence of a nonradial solution for α large and N ≥ 4. In this paper, we show the existence of a nonradial solution for any α > 0 and N ≥ 4. Furthermore, we prove that equation (*) has infinitely many nonradial solutions, whose energy can be made arbitrarily large.