The Existence Of Positive Solutions For The Neumann Problem Of Elliptic Systems With Sobolev Critical Exponent

In this paper, we study the following Neumann boundary problem with Sobolev critical exponent where α,β> 1,α+β=2*:=2N/(N-2)(N≥3) and Ω, is a bounded domain in RN(N≥3) with αΩ∈C2, n denote the unit outward normal vector at boundary αΩ.. We prove the existence of positive solutions of the above elliptic system for some ranges of the parameters α,β, N and λ.