A Complete Analysis of a Model Nonlinear Singular Perturbation Problem Having a Continuous Locus of Singular Points

摘要

Consider the boundary value problem epsilon y double prime = (y sq - t sq) y', -1 < t < 0, y(-1) = A, y(0) = B. Depending on the choice of A and B, one can insure the existence of 'turning points'. However, due to the nonlinear nature of the problem, one does not know the position or number of such turning points. In the case when A > 0 = B Kedem, Parter and Steuerwalt gave a development of this problem based on an abstract bifurcation analysis which in turn was based on 'degree theory'. In this paper we give a complete analysis of the problem based entirely on a -priori estimates and the 'shooting' method.