A boundary value problem for a nonlinear differential equation with a small parameter

Abstract

(1) f(X, U)u' + g(X, u) = 0 has a solution u(x) on O O, which includes the point (0, yo). (iii) There exists a constant k > 0 such that f(x, y) ? k for (x, y) in R. Then, for all sufficiently small e>0, there exists in R a solution y(x) = y(x, e) of (2) ey + f(x, y)y' + g(x, y) = 0 satisfying the boundary conditions