Nonlocal problems at nearly critical growth

We study the asymptotic behavior of solutions to the nonlocal nonlinear equation (-Delta(p))(s)u = vertical bar u vertical bar(q-2)u in a bounded domain Omega subset of R-N as q approaches the critical Sobolev exponent p* = Np/(N - ps). We prove that ground state solutions concentrate at a single point (x) over bar epsilon (Omega) over bar and analyze the asymptotic behavior for sequences of solutions at higher energy levels. In the semi-linear case p = 2, we prove that for smooth domains the concentration point (x) over bar cannot lie on the boundary, and identify its location in the case of annular domains