Solutions with spikes at the boundary for a 2D nonlinear Neumann problem with large exponent

We consider the elliptic equation −Δu+u=0 in a bounded, smooth domain Ω in R2, subject to the nonlinear Neumann boundary condition . Here p>1 is a large parameter. We prove that given any integer m⩾1 there exist at least two families of solutions up developing exactly m peaks ξi∈∂Ω, in the sense that , as p→∞.