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

AbstractWe consider a system of the form −ε2Δu+u=g(v),−ε2Δv+v=f(u) in Ω with Neumann boundary condition on ∂Ω, where Ω is a smooth bounded domain in RN,N⩾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 ε goes to zero, at a point of the boundary which maximizes the mean curvature of the boundary of Ω