A Schrödinger singular perturbation problem

Consider the equation −ε2Δuε + q(x)uε = f(uε) in R3R3, ∣u(∞)∣ < ∞, ε = const > 0. Under what assumptions on q(x) and f(u) can one prove that the solution uε exists and limε→0uε = u(x), where u(x) solves the limiting problem q(x)u = f(u)? These are the questions discussed in the paper.