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We prove the existence of nonconstant positive solutions for a system of the form -ε2Δu + u = g(v), -ε2Δv + v = f(u) in Ω, with Neumann boundary conditions on ∂Ω, where Ω is a smooth bounded domain and f, g are power-type nonlinearities having superlinear and subcritical growth at infinity. For small values of ε, the corresponding solutions uε and vε admit a unique maximum point which is located at the boundary of Ω. ©2004 American Mathematical Society.

Spike-layered solutions for an elliptic system with Neumann boundary conditions