Asymptotic behavior of interior peaked solutions for a slightly subcritical Neumann problem

In this paper, we study the asymptotic behavior of solutions of the Neumann problem ( P ɛ ) : − Δ u + V ( x ) u = u p − ɛ , u > 0 in Ω , ∂ u / ∂ ν = 0 on ∂ Ω , where Ω is a smooth bounded domain in R n , n ≥ 6 , p + 1 = 2 n / ( n − 2 ) is the critical Sobolev exponent, ɛ is a small positive real and V is a smooth positive function defined on Ω ¯ . We give a precise location of interior blow up points and blow up rates when the number of concentration points is less than or equal to 2. The proof strategy is based on a refined blow up analysis in the neighborhood of bubbles.