Existence and multiplicity of positive solutions for Neumann problems involving singularity and critical growth

In this paper, the existence and multiplicity of positive solutions is established for a class of Numann problems of the form{−Δu=u2⁎−1+λuγ,in Ω,∂u∂ν=0,on ∂Ω, here Ω is a smooth bounded domain in RN, N≥3, 2⁎=2NN−2, γ∈(0,1) and λ>0 is a real parameter, ∂∂ν is the outer normal derivative. The main technical approach is based on the variational and perturbation methods.