  We study the monic orthogonal polynomials with respect to a singularly
perturbed Airy weight. By using Chen and Ismail's ladder operator approach, we
derive a discrete system satisfied by the recurrence coefficients for the
orthogonal polynomials. We find that the orthogonal polynomials satisfy a
second-order linear ordinary differential equation, whose coefficients are all
expressed in terms of the recurrence coefficients. By considering the time
evolution, we obtain a system of differential-difference equations satisfied by
the recurrence coefficients. Finally, we study the asymptotics of the
recurrence coefficients when the degrees of the orthogonal polynomials tend to
infinity.
