Locating the peaks of the least energy solutions to an ellyptic system with Neumann boundary conditions

We consider a system of the form -epsilon(2)Deltau + u = g(v), -epsilon(2)Deltav + u = f(u) in Omega with Neumann boundary condition on partial derivativeOmega, where Omega is a smooth bounded domain in R-N, N greater than or equal to 3 and f, g are power-type nonlinearities having superlinear and subcritical growth at infinity. We prove that the least energy solutions to such a system concentrate, as epsilon goes to zero, at a point of the boundary which maximizes the mean curvature of the boundary of Q. (C) 2004 Elsevier Inc. All rights reserved.