Remarks on Singular Perturbations with Turning Points

Boundary value problems are considered for the differential equation ε y'' + f(x,ε )y' + g(x,ε )y' + g(x,ε )y = 0, where f(x,ε )x < 0 for x ≠ 0. Let \ y(x,ε ₙ )\ converge to y(x) as ε ₙ → 0 +. In rare situations y(x) ≡ 0. This report studies such a phenomenon.