Infinitely many solutions for an elliptic Neumann problem involving critical Sobolev growth

In this paper, we prove the existence of infinitely many solutions for the following elliptic problem with critical Sobolev growth:−Δu=|u|2⁎−2u+g(u)in Ω,∂u∂ν=0on ∂Ω, where Ω   is a bounded domain in RNRN with C3C3 boundary, N⩾3N⩾3, ν is the outward unit normal of ∂Ω  , 2⁎=2NN−2, and g(t)=μ|t|p−2t−tg(t)=μ|t|p−2t−t, or g(t)=μtg(t)=μt, where p∈(2,2⁎)p∈(2,2⁎), μ>0μ>0 are constants. We obtain the existence of infinitely many solutions under certain assumptions on N, p and ∂Ω  . In particular, if g(t)=μtg(t)=μt with μ>0μ>0, N⩾7N⩾7, and Ω is a strictly convex domain, then the problem has infinitely many solutions.