A Singularly Perturbed Nonlinear Boundary Value Problem

In this paper, a singularly perturbed nonlinear problem ϵy″ − ƒ(x, y, y′) = 0, 0 < x < 1, 0 < ϵ < < 1,y(0) = A, y(1) = B, where y, ƒ, A, and B are n-dimensional vector is considered. Under the appropriate assumptions the author proves that there exists a solution y(x, ϵ) and the estimation of y(x, ϵ) is obtained using the method of differential inequalities.