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

In this paper, we are concerned with the following two coupled Schrödinger systems in a bounded domain Ω ⊂ R N ( N = 2 , 3 ) with Neumann boundary conditions { − ε 2 Δ u + u = μ 1 u 3 + β u v 2 , − ε 2 Δ v + v = μ 2 v 3 + β u 2 v , u > 0 , v > 0 , ∂ u / ∂ n = 0 , ∂ v / ∂ n = 0 , on  ∂ Ω . Suppose the mean curvature H ( P ) of the boundary ∂ Ω 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.