GEOMETRIC APPROACH TO BOUNDARY-LAYER PROBLEMS EXHIBITING RESONANCE

The boundary value problem is considered for the singularly perturbed equation epsilon y double prime plus f(x, epsilon )y prime plus g(x, epsilon )y equals 0 under the assumption that f changes sign and f//x less than 0. It is shown that this problem can be understood by imbedding the equation in a two parameter family epsilon y double prime plus f(x, epsilon , delta )y prime plus g(x, epsilon , delta )y equals 0. Under a transversality condition on f and g, delta equals delta ( epsilon ) is computed so that the latter equation displays resonance. The same techniques are used to show that B. J. Matkowsky's criteria provide a simple and effective way to compute the Taylor series of delta ( epsilon ).