The Solutions of a Model Nonlinear Singular Perturbation Problem Having A Continuous Locus of Singular Points

Consider the boundary value problem εy″ =(y² ? t²)y′, ?1 ?t?0, y(?1) = A, y(0) = B. We discuss the multiplicity of solutions and their limiting behavior as ε→+0+ for certain choices of A and B. In particular, when A = 1, B = 0, a bifurcation analysis gives a detailed and fairly complete analysis. The interest here arises from the complexity of the set of "turning points."