Abstract

We consider the elliptic equation - ? u + u = 0 in a bounded, smooth domain O in R2, subject to the nonlinear Neumann boundary condition frac(? u, ? ?) = up. 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 ?i ? ? O, in the sense that p up ? 2 e p ?i = 1 m d?i, as p ? 8. © 2009 Elsevier Inc. All rights reserved.