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We are interested in standing wave solutions of the dimensionless nonlinear Schr(o)dinger equation iΦt(x,t) = -△zΦ + V (x)Φ + f(x,Φ),x ∈ RN,t ∈ R,(NLS) when the potential V: RN → R is close to an infinite well potential V∞: RN → R,i.e.V∞ = ∞ on an exterior domain RN \Ω,V∞| Ω∈ L∞(Ω ).The nonlinearity f may be of Gross-Pitaevskii type.