Solution to Singularly Perturbed Boundary Value Problems by the Duck Hunting Method

A situation is analyzed when two different curves of slow motion intersect in a general way in a two-dimensional relaxation system. It is shown that this situation gives rise to the so-called duck trajectories. The results of the analysis are applied to the construction of the asymptotics of the principal eigenvalue of the Dirichlet problem for a singularly perturbed Schrödinger equation.