ON BOUNDARY LAYER PROBLEMS EXHIBITING RESONANCE.

Singularly perturbed boundary value problems are considered for differential equations of the form epsilon y double prime plus f(x; epsilon )y prime plus g(x, epsilon )y equals h(x , epsilon ), where f changes sign at one or more points in the interval under consideration. Such points are sometimes referred to as turning points. It is shown that various anomalies can occur in such problems. One of these anomalies is the phenomenon of resonance. Criteria are presented for resonance to occur, and uniformly valid asymptotic expansions for the solution of such problems are derived.