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We are interested in the existence of standing waves for the nonlinear Klein Gordon equation ε 2 □ψ + Wʹ(ψ) = 0 in a bounded domain D. A standing wave has the form ψ(t, x) = u(x)e- iwt/ε ; for these solutions the Klein Gordon equation becomes

Semiclassical Limit For the Nonlinear Klein Gordon Equation in Bounded Domains