How Many Jumps. Variational Characterization of the Limit Solution of a Singular Perturbation Problem

摘要

Two alternative methods are used to describe the limiting behaviour, as sigma decreases, approaching the limit of 0, of the solution y sub sigma of the nonlinear two point boundary value problem sigma double prime + (g-y) y prime = 0, y(0) = 0, y(1), where g is a given function. The first method is based on the theory of maximal monotone operators, whereas the second one uses duality theory.