Multi-peak solutions to coupled Schrodinger systems with Neumann boundary conditions

In this paper, we are concerned with the following two coupled Schrodinger systems in a bounded domain Omega subset of R-N (N = 2,3) with Neumann boundary conditions. -epsilon(2) s2 Delta u + u = mu 1u(3) + beta uv(2), -epsilon(2) Delta V + v = mu(2)v(3) + beta u(2)v, u > 0, v > 0, a partial derivative/partial derivative n = 0, partial derivative v/partial derivative an = 0, on partial derivative 2. Suppose the mean curvature H(P) of the boundary 0s7 has several local minimums or local 'maximums, we obtain the existence of solutions with multi-peaks to the system with all peaks being on the boundary and all peaks locate either near the local maxima or near the local minima of the mean curvature at the boundary of the domain. (C) 2013 Elsevier Inc. All rights reserved.