On an internal boundary layer problem

摘要

In this paper, we consider the boundary value problemεy″+a(x)y′+b(x)y=0,x∈[x−,x+],x−<00 and β/α≠1,2,3,…. Under certain smoothness conditions on a(x) and b(x), an asymptotic solution is constructed, which holds uniformly for x∈[x−,x+]. This result is proved rigorously by using the method of successive approximation.