Abstract: Consider the equation −ε 2 Δu ε + q(x)u ε = f(u ε ) in , ∣u(∞)∣<∞, ε =const>0. Under what assumptions on q(x) and f(u) can one prove that the solution u ε exists and lim ε→0 u ε = u(x), where u(x) solves the limiting problem q(x)u = f(u)? These are the questions discussed in the paper. [Copyright &y& Elsevier]