A Class Of Singular Perturbations For Second Order Linear Turning Point Boundary Value Problems With High Order On Infinite Interval

Singular perturbation problem with Turning Point has been one of the most important object of study today, a vast majority of problems in quantum physics are of them, such as the famous Schrodinger equation. Turning point in singular perturbation has been a difficult problem, mainly because the behavior of the so-lutions near the turning point has changed. The Boundary Function Method for singular perturbation problems becomes invalid since it does not satisfy the stabil-ity condition. Current literatures have mainly examined the linear turning point for first-order problems, and normally only discussed the zero-th asymptotic expansion of the solutions.In this paper, a class of singular perturbations for second order linear turning point boundary value problems with high order on infinite interval, which encoun-tered in Non-Newtonian boundary layer calculation of collision problem, is consid-ered. Using the matching of asymptotic expansions, the formal asymptotic solution is constructed. By using the theory of differential inequality the uniform validity of the asymptotic expansion for the solution is proved.