A CLASS OF BOUNDARY VALUE PROBLEMS OF SINGULARLY PERTURBED EQUATION WITH TURNING POINT

We consider the existence and asymptotic behavior of singularly perturbed boundary value problem;εX″= b（X,t）X′,t ∈（0, 1）（1）X（0） =α, X（1） =β, （2）where, ε】0, is a sufficiently small parameter, b（X,t） is continuous in R×[0,1 ],α,βare prescribedboundary condition, and there is a function X0（t） satisfying the implicit equation b[X0（t）,t] 0t∈[0,1 ].Boundary value problem in this case is rarely studied by other mathematician, the auther has ever dis-cussed the autonomous equation corresponding the boundary value problem （1）,（2）. Generally speaking,the solution of the corresponding problem has boundary layer at each end of the time interval [0 ,1] , itsinner solution is commposed by one or several constant function, these constant is the zero point of the au-